Q21 of 45 Page 1

Prove the following:


OR


Solve for x: 2 tan-1(cos x) = tan-1(2cosec x)

Given:


Rationalizing the denominator,








= cot-1 (cot x/2)


= x/2


= RHS


Hence proved.


OR


Given: 2 tan-1 (cos x) = tan-1 (2 csc x)


We know that





⇒ sin x cos x = sin2 x


⇒ sin x (cos x – sin x) = 0


⇒ sin x = 0 or cos x – sin x = 0


⇒ sin x = cos x


⇒ tan x = 1


∴ x = 0 or π/4


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