Trigonometry Examples

$\frac{\cot (x) - \tan (x)}{1 - 2 \sin^{2} (x)}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

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

Step 2

Apply the cosine double-angle identity.

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

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

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

Step 3.2

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

$\frac{\cot (x) - \tan (x)}{\cos (2 x)}$