JEE inverse trigo

Geometry Level 4

Find the value of t a n − 1 ( t a n 2 A 2 ) + t a n − 1 ( c o t A ) + t a n − 1 ( c o t 3 A ) tan^{-1}(\frac{tan2A}{2})+tan^{-1}(cotA)+tan^{-1}(cot^{3}A) ,if 0 < A < π 4 0<A<\frac{\pi}{4}

π 2 \frac{\pi}{2} π \pi 1 0

Tanishq Varshney by Tanishq Varshney , 23, India

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1 solution

Raj Rajput
May 2, 2015

for saving time in JEE take value of A= pi/6 then proceed simplify ,it becomes tan inverse ((root 3)/2) +tan inverse (root 3)+tan inverse (3 * (root 3)) , add first two applying

tan inverse A + tan inverse B = pi + tan inverse ( A+B/1-A*B)

when A*B > 1 comes out to be pi ... :) :)

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