Question

verify the identity

tan 0-cot 0 / tan 0 + cot 0 (not on the same line) + 2cos^2 0=1

Answer 1

Answer:

See below for the proof of the identity

Step-by-step explanation:

I read your statement as $\displaystyle \frac{\tan\theta-\cot\theta}{\tan\theta+\cot\theta}+2\cos^2\theta=1$:

$\displaystyle \frac{\tan\theta-\cot\theta}{\tan\theta+\cot\theta}+2\cos^2\theta\\\\\frac{\frac{\sin\theta}{\cos\theta}-\frac{\cos\theta}{\sin\theta}}{\frac{\sin\theta}{\cos\theta}+\frac{\cos\theta}{\sin\theta}} +2\cos^2\theta\\\\\frac{\frac{\sin^2\theta-\cos^2\theta}{\sin\theta\cos\theta}}{\frac{\sin^2\theta+\cos^2\theta}{\sin\theta\cos\theta}} +2\cos^2\theta\\\\\frac{\frac{\sin^2\theta-\cos^2\theta}{\sin\theta\cos\theta}}{\frac{1}{\sin\theta\cos\theta}} +2\cos^2\theta$

$\displaystyle \sin^2\theta-\cos^2\theta+2\cos^2\theta\\\\\sin^2\theta+\cos^2\theta\\\\1$

Thus, the identity is proven.