Trigonometry Examples

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

Step 1

Rewrite $\sec (x - 1)$ in terms of sines and cosines.

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

Step 2

Simplify the expression.

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Step 2.1

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

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

Step 2.2

One to any power is one.

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

Step 3

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

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

Step 4

Multiply by $1$ .

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

Step 5

Separate fractions.

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

Step 6

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

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

Step 7

Divide $\cos^{2} (x)$ by $1$ .

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