Prove $tan^-1 (cot (theta)) /2 = pi/4 + theta/2$ ?

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Answer 1 · 2018-03-19T02:34:19

I answer will be like that:

$L.H.S=(tan^(-1)(cottheta))/2$

$=-(tan^(-1)(tan(pi/2+theta))/2)$

$=-((pi/2+theta)/2)$

$=-(pi/4+theta/2)=R.H.S$

Prove tan^-1 (cot (theta)) /2 = pi/4 + theta/2tan^-1 (cot (theta)) /2 = pi/4 + theta/2?