Trigonometry Examples

$2 \tan (x) \cos^{2} (x) = 1$

Step 1

Simplify $2 \tan (x) \cos^{2} (x)$ .

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Step 1.1

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

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

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $2$ and $\frac{\sin (x)}{\cos (x)}$ .

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

Step 1.2.2

Cancel the common factor of $\cos (x)$ .

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Step 1.2.2.1

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

$\frac{2 \sin (x)}{\cos (x)} (\cos (x) \cos (x)) = 1$

Step 1.2.2.2

Cancel the common factor.

$\frac{2 \sin (x)}{\cos (x)} (\cos (x) \cos (x)) = 1$

Step 1.2.2.3

Rewrite the expression.

$2 \sin (x) \cos (x) = 1$

Step 1.3

Apply the sine double-angle identity.

$\sin (2 x) = 1$

Step 2

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

$x = \frac{π}{4} + π n$ , for any integer $n$

Step 3