Trigonometry Examples

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

Step 1

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

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Step 1.1

Apply pythagorean identity.

$\cos^{2} (x) \tan^{2} (x) = \sin^{2} (x)$

Step 1.2

Rewrite $\tan (x)$ in terms of sines and cosines.

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

Step 1.3

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

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

Step 1.4

Cancel the common factor of $\cos^{2} (x)$ .

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Step 1.4.1

Cancel the common factor.

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

Step 1.4.2

Rewrite the expression.

$\sin^{2} (x) = \sin^{2} (x)$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 0, 0.1, - 0.3, 0.3, - \frac{2}{5}, \frac{2}{5}, - \frac{1}{2}$

Step 3