Trigonometry Examples

$\sec^{2} (x - 1)$

Step 1

Separate negation.

$\sec^{2} (x - (1))$

Step 2

Apply the difference of angles identity.

${(\frac{\sec (x) \sec (1) \csc (x) \csc (1)}{\csc (x) \csc (1) + \sec (x) \sec (1)})}^{2}$

Step 3

Simplify the numerator.

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Step 3.1

Evaluate $\sec (1)$ .

${(\frac{\sec (x) \cdot 1.85081571 \csc (x) \csc (1)}{\csc (x) \csc (1) + \sec (x) \sec (1)})}^{2}$

Step 3.2

Evaluate $\csc (1)$ .

${(\frac{\sec (x) \cdot 1.85081571 \csc (x) \cdot 1.1883951}{\csc (x) \csc (1) + \sec (x) \sec (1)})}^{2}$

Step 3.3

Multiply $1.1883951$ by $1.85081571$ .

${(\frac{\sec (x) \cdot 2.19950034 \csc (x)}{\csc (x) \csc (1) + \sec (x) \sec (1)})}^{2}$

Step 4

Simplify the denominator.

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Step 4.1

Evaluate $\csc (1)$ .

${(\frac{\sec (x) \cdot 2.19950034 \csc (x)}{\csc (x) \cdot 1.1883951 + \sec (x) \sec (1)})}^{2}$

Step 4.2

Move $1.1883951$ to the left of $\csc (x)$ .

${(\frac{\sec (x) \cdot 2.19950034 \csc (x)}{1.1883951 \cdot \csc (x) + \sec (x) \sec (1)})}^{2}$

Step 4.3

Evaluate $\sec (1)$ .

${(\frac{\sec (x) \cdot 2.19950034 \csc (x)}{1.1883951 \csc (x) + \sec (x) \cdot 1.85081571})}^{2}$

Step 4.4

Move $1.85081571$ to the left of $\sec (x)$ .

${(\frac{\sec (x) \cdot 2.19950034 \csc (x)}{1.1883951 \csc (x) + 1.85081571 \sec (x)})}^{2}$

Step 5

Move $2.19950034$ to the left of $\sec (x)$ .

${(\frac{2.19950034 \cdot \sec (x) \csc (x)}{1.1883951 \csc (x) + 1.85081571 \sec (x)})}^{2}$

Step 6

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 6.1

Apply the product rule to $\frac{2.19950034 \sec (x) \csc (x)}{1.1883951 \csc (x) + 1.85081571 \sec (x)}$ .

$\frac{{(2.19950034 \sec (x) \csc (x))}^{2}}{{(1.1883951 \csc (x) + 1.85081571 \sec (x))}^{2}}$

Step 6.2

Apply the product rule to $2.19950034 \sec (x) \csc (x)$ .

$\frac{{(2.19950034 \sec (x))}^{2} \csc^{2} (x)}{{(1.1883951 \csc (x) + 1.85081571 \sec (x))}^{2}}$

Step 6.3

Apply the product rule to $2.19950034 \sec (x)$ .

$\frac{{2.19950034}^{2} \sec^{2} (x) \csc^{2} (x)}{{(1.1883951 \csc (x) + 1.85081571 \sec (x))}^{2}}$

Step 7

Raise $2.19950034$ to the power of $2$ .

$\frac{4.83780174 \sec^{2} (x) \csc^{2} (x)}{{(1.1883951 \csc (x) + 1.85081571 \sec (x))}^{2}}$