Algebra Examples

$\sec^{2} (\frac{π}{2} - x) (\sin^{2} (x) - \sin^{4} (x))$

Step 1

Rewrite $\sec (\frac{π}{2} - x)$ in terms of sines and cosines.

${(\frac{1}{\cos (\frac{π}{2} - x)})}^{2} (\sin^{2} (x) - \sin^{4} (x))$

Step 2

Simplify the expression.

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Step 2.1

Apply the product rule to $\frac{1}{\cos (\frac{π}{2} - x)}$ .

$\frac{1^{2}}{\cos^{2} (\frac{π}{2} - x)} (\sin^{2} (x) - \sin^{4} (x))$

Step 2.2

One to any power is one.

$\frac{1}{\cos^{2} (\frac{π}{2} - x)} (\sin^{2} (x) - \sin^{4} (x))$

Step 3

Apply the distributive property.

$\frac{1}{\cos^{2} (\frac{π}{2} - x)} \sin^{2} (x) + \frac{1}{\cos^{2} (\frac{π}{2} - x)} (- \sin^{4} (x))$

Step 4

Combine $\frac{1}{\cos^{2} (\frac{π}{2} - x)}$ and $\sin^{2} (x)$ .

$\frac{\sin^{2} (x)}{\cos^{2} (\frac{π}{2} - x)} + \frac{1}{\cos^{2} (\frac{π}{2} - x)} (- \sin^{4} (x))$

Step 5

Rewrite using the commutative property of multiplication.

$\frac{\sin^{2} (x)}{\cos^{2} (\frac{π}{2} - x)} - \frac{1}{\cos^{2} (\frac{π}{2} - x)} \sin^{4} (x)$

Step 6

Combine $\sin^{4} (x)$ and $\frac{1}{\cos^{2} (\frac{π}{2} - x)}$ .

$\frac{\sin^{2} (x)}{\cos^{2} (\frac{π}{2} - x)} - \frac{\sin^{4} (x)}{\cos^{2} (\frac{π}{2} - x)}$

Step 7

Rewrite $\frac{\sin^{2} (x)}{\cos^{2} (\frac{π}{2} - x)}$ as ${(\frac{\sin (x)}{\cos (\frac{π}{2} - x)})}^{2}$ .

${(\frac{\sin (x)}{\cos (\frac{π}{2} - x)})}^{2} - \frac{\sin^{4} (x)}{\cos^{2} (\frac{π}{2} - x)}$

Step 8

Rewrite $\frac{\sin^{4} (x)}{\cos^{2} (\frac{π}{2} - x)}$ as ${(\frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})}^{2}$ .

${(\frac{\sin (x)}{\cos (\frac{π}{2} - x)})}^{2} - {(\frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})}^{2}$

Step 9

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \frac{\sin (x)}{\cos (\frac{π}{2} - x)}$ and $b = \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)}$ .

$(\frac{\sin (x)}{\cos (\frac{π}{2} - x)} + \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)}) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10

Simplify terms.

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Step 10.1

Simplify each term.

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Step 10.1.1

Rewrite $\frac{\sin (x)}{\cos (\frac{π}{2} - x)}$ as a product.

$(\sin (x) \frac{1}{\cos (\frac{π}{2} - x)} + \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)}) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.2

Write $\sin (x)$ as a fraction with denominator $1$ .

$(\frac{\sin (x)}{1} \cdot \frac{1}{\cos (\frac{π}{2} - x)} + \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)}) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.3

Simplify.

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Step 10.1.3.1

Divide $\sin (x)$ by $1$ .

$(\sin (x) \frac{1}{\cos (\frac{π}{2} - x)} + \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)}) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.3.2

Convert from $\frac{1}{\cos (\frac{π}{2} - x)}$ to $\sec (\frac{π}{2} - x)$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)}) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.4

Factor $\sin (x)$ out of $\sin^{2} (x)$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \frac{\sin (x) \sin (x)}{\cos (\frac{π}{2} - x)}) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.5

Separate fractions.

$(\sin (x) \sec (\frac{π}{2} - x) + \frac{\sin (x)}{1} \cdot \frac{\sin (x)}{\cos (\frac{π}{2} - x)}) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.6

Rewrite $\frac{\sin (x)}{\cos (\frac{π}{2} - x)}$ as a product.

$(\sin (x) \sec (\frac{π}{2} - x) + \frac{\sin (x)}{1} (\sin (x) \frac{1}{\cos (\frac{π}{2} - x)})) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.7

Write $\sin (x)$ as a fraction with denominator $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \frac{\sin (x)}{1} (\frac{\sin (x)}{1} \cdot \frac{1}{\cos (\frac{π}{2} - x)})) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.8

Simplify.

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Step 10.1.8.1

Divide $\sin (x)$ by $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \frac{\sin (x)}{1} (\sin (x) \frac{1}{\cos (\frac{π}{2} - x)})) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.8.2

Convert from $\frac{1}{\cos (\frac{π}{2} - x)}$ to $\sec (\frac{π}{2} - x)$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \frac{\sin (x)}{1} (\sin (x) \sec (\frac{π}{2} - x))) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.9

Divide $\sin (x)$ by $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin (x) (\sin (x) \sec (\frac{π}{2} - x))) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.10

Multiply $\sin (x) (\sin (x) \sec (\frac{π}{2} - x))$ .

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Step 10.1.10.1

Raise $\sin (x)$ to the power of $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{1} (x) \sin (x) \sec (\frac{π}{2} - x)) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.10.2

Raise $\sin (x)$ to the power of $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{1} (x) \sin^{1} (x) \sec (\frac{π}{2} - x)) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.10.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(\sin (x) \sec (\frac{π}{2} - x) + {\sin (x)}^{1 + 1} \sec (\frac{π}{2} - x)) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.1.10.4

Add $1$ and $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\frac{\sin (x)}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.2

Simplify each term.

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Step 10.2.1

Rewrite $\frac{\sin (x)}{\cos (\frac{π}{2} - x)}$ as a product.

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \frac{1}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.2.2

Write $\sin (x)$ as a fraction with denominator $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\frac{\sin (x)}{1} \cdot \frac{1}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.2.3

Simplify.

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Step 10.2.3.1

Divide $\sin (x)$ by $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \frac{1}{\cos (\frac{π}{2} - x)} - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.2.3.2

Convert from $\frac{1}{\cos (\frac{π}{2} - x)}$ to $\sec (\frac{π}{2} - x)$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - \frac{\sin^{2} (x)}{\cos (\frac{π}{2} - x)})$

Step 10.2.4

Factor $\sin (x)$ out of $\sin^{2} (x)$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - \frac{\sin (x) \sin (x)}{\cos (\frac{π}{2} - x)})$

Step 10.2.5

Separate fractions.

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - (\frac{\sin (x)}{1} \cdot \frac{\sin (x)}{\cos (\frac{π}{2} - x)}))$

Step 10.2.6

Rewrite $\frac{\sin (x)}{\cos (\frac{π}{2} - x)}$ as a product.

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - (\frac{\sin (x)}{1} (\sin (x) \frac{1}{\cos (\frac{π}{2} - x)})))$

Step 10.2.7

Write $\sin (x)$ as a fraction with denominator $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - (\frac{\sin (x)}{1} (\frac{\sin (x)}{1} \cdot \frac{1}{\cos (\frac{π}{2} - x)})))$

Step 10.2.8

Simplify.

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Step 10.2.8.1

Divide $\sin (x)$ by $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - (\frac{\sin (x)}{1} (\sin (x) \frac{1}{\cos (\frac{π}{2} - x)})))$

Step 10.2.8.2

Convert from $\frac{1}{\cos (\frac{π}{2} - x)}$ to $\sec (\frac{π}{2} - x)$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - (\frac{\sin (x)}{1} (\sin (x) \sec (\frac{π}{2} - x))))$

Step 10.2.9

Divide $\sin (x)$ by $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - (\sin (x) (\sin (x) \sec (\frac{π}{2} - x))))$

Step 10.2.10

Multiply $\sin (x) (\sin (x) \sec (\frac{π}{2} - x))$ .

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Step 10.2.10.1

Raise $\sin (x)$ to the power of $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - (\sin^{1} (x) \sin (x) \sec (\frac{π}{2} - x)))$

Step 10.2.10.2

Raise $\sin (x)$ to the power of $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - (\sin^{1} (x) \sin^{1} (x) \sec (\frac{π}{2} - x)))$

Step 10.2.10.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - ({\sin (x)}^{1 + 1} \sec (\frac{π}{2} - x)))$

Step 10.2.10.4

Add $1$ and $1$ .

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - (\sin^{2} (x) \sec (\frac{π}{2} - x)))$

$(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 11

Expand $(\sin (x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x)) (\sin (x) \sec (\frac{π}{2} - x) - \sin^{2} (x) \sec (\frac{π}{2} - x))$ using the FOIL Method.

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Step 11.1

Apply the distributive property.

$\sin (x) \sec (\frac{π}{2} - x) (\sin (x) \sec (\frac{π}{2} - x) - \sin^{2} (x) \sec (\frac{π}{2} - x)) + \sin^{2} (x) \sec (\frac{π}{2} - x) (\sin (x) \sec (\frac{π}{2} - x) - \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 11.2

Apply the distributive property.

$\sin (x) \sec (\frac{π}{2} - x) (\sin (x) \sec (\frac{π}{2} - x)) + \sin (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x)) + \sin^{2} (x) \sec (\frac{π}{2} - x) (\sin (x) \sec (\frac{π}{2} - x) - \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 11.3

Apply the distributive property.

Step 12

Simplify terms.

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Step 12.1

Combine the opposite terms in $\sin (x) \sec (\frac{π}{2} - x) (\sin (x) \sec (\frac{π}{2} - x)) + \sin (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x)) + \sin^{2} (x) \sec (\frac{π}{2} - x) (\sin (x) \sec (\frac{π}{2} - x)) + \sin^{2} (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x))$ .

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Step 12.1.1

Reorder the factors in the terms $\sin (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x))$ and $\sin^{2} (x) \sec (\frac{π}{2} - x) (\sin (x) \sec (\frac{π}{2} - x))$ .

$\sin (x) \sec (\frac{π}{2} - x) (\sin (x) \sec (\frac{π}{2} - x)) - \sin^{2} (x) \sec (\frac{π}{2} - x) \sec (\frac{π}{2} - x) \sin (x) + \sin^{2} (x) \sec (\frac{π}{2} - x) \sec (\frac{π}{2} - x) \sin (x) + \sin^{2} (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 12.1.2

Add $- \sin^{2} (x) \sec (\frac{π}{2} - x) \sec (\frac{π}{2} - x) \sin (x)$ and $\sin^{2} (x) \sec (\frac{π}{2} - x) \sec (\frac{π}{2} - x) \sin (x)$ .

$\sin (x) \sec (\frac{π}{2} - x) (\sin (x) \sec (\frac{π}{2} - x)) + 0 + \sin^{2} (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 12.1.3

Add $\sin (x) \sec (\frac{π}{2} - x) (\sin (x) \sec (\frac{π}{2} - x))$ and $0$ .

$\sin (x) \sec (\frac{π}{2} - x) (\sin (x) \sec (\frac{π}{2} - x)) + \sin^{2} (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 12.2

Simplify each term.

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Step 12.2.1

Multiply $\sin (x) \sec (\frac{π}{2} - x) (\sin (x) \sec (\frac{π}{2} - x))$ .

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Step 12.2.1.1

Raise $\sin (x)$ to the power of $1$ .

$\sin^{1} (x) \sin (x) \sec (\frac{π}{2} - x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 12.2.1.2

Raise $\sin (x)$ to the power of $1$ .

$\sin^{1} (x) \sin^{1} (x) \sec (\frac{π}{2} - x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 12.2.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\sin (x)}^{1 + 1} \sec (\frac{π}{2} - x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 12.2.1.4

Add $1$ and $1$ .

$\sin^{2} (x) \sec (\frac{π}{2} - x) \sec (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 12.2.1.5

Raise $\sec (\frac{π}{2} - x)$ to the power of $1$ .

$\sin^{2} (x) (\sec^{1} (\frac{π}{2} - x) \sec (\frac{π}{2} - x)) + \sin^{2} (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 12.2.1.6

Raise $\sec (\frac{π}{2} - x)$ to the power of $1$ .

$\sin^{2} (x) (\sec^{1} (\frac{π}{2} - x) \sec^{1} (\frac{π}{2} - x)) + \sin^{2} (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 12.2.1.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sin^{2} (x) {\sec (\frac{π}{2} - x)}^{1 + 1} + \sin^{2} (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 12.2.1.8

Add $1$ and $1$ .

$\sin^{2} (x) \sec^{2} (\frac{π}{2} - x) + \sin^{2} (x) \sec (\frac{π}{2} - x) (- \sin^{2} (x) \sec (\frac{π}{2} - x))$

Step 12.2.2

Rewrite using the commutative property of multiplication.

$\sin^{2} (x) \sec^{2} (\frac{π}{2} - x) - \sin^{2} (x) \sec (\frac{π}{2} - x) \sin^{2} (x) \sec (\frac{π}{2} - x)$

Step 12.2.3

Multiply $\sin^{2} (x)$ by $\sin^{2} (x)$ by adding the exponents.

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Step 12.2.3.1

Move $\sin^{2} (x)$ .

$\sin^{2} (x) \sec^{2} (\frac{π}{2} - x) - (\sin^{2} (x) \sin^{2} (x)) \sec (\frac{π}{2} - x) \sec (\frac{π}{2} - x)$

Step 12.2.3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sin^{2} (x) \sec^{2} (\frac{π}{2} - x) - {\sin (x)}^{2 + 2} \sec (\frac{π}{2} - x) \sec (\frac{π}{2} - x)$

Step 12.2.3.3

Add $2$ and $2$ .

$\sin^{2} (x) \sec^{2} (\frac{π}{2} - x) - \sin^{4} (x) \sec (\frac{π}{2} - x) \sec (\frac{π}{2} - x)$

Step 12.2.4

Multiply $- \sin^{4} (x) \sec (\frac{π}{2} - x) \sec (\frac{π}{2} - x)$ .

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Step 12.2.4.1

Raise $\sec (\frac{π}{2} - x)$ to the power of $1$ .

$\sin^{2} (x) \sec^{2} (\frac{π}{2} - x) - \sin^{4} (x) (\sec^{1} (\frac{π}{2} - x) \sec (\frac{π}{2} - x))$

Step 12.2.4.2

Raise $\sec (\frac{π}{2} - x)$ to the power of $1$ .

$\sin^{2} (x) \sec^{2} (\frac{π}{2} - x) - \sin^{4} (x) (\sec^{1} (\frac{π}{2} - x) \sec^{1} (\frac{π}{2} - x))$

Step 12.2.4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sin^{2} (x) \sec^{2} (\frac{π}{2} - x) - \sin^{4} (x) {\sec (\frac{π}{2} - x)}^{1 + 1}$

Step 12.2.4.4

Add $1$ and $1$ .

$\sin^{2} (x) \sec^{2} (\frac{π}{2} - x) - \sin^{4} (x) \sec^{2} (\frac{π}{2} - x)$