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Question
Solve the following equation:
2 tan−1 (cos x) = tan−1 (2 cosec x)
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Solution
2 tan−1 (cos x) = tan−1 (2 cosec x)
⇒ `tan^(-1) ((2 cos x)/(1- cos^2 x)) = tan^(-1) (2 "cosec x")`
⇒ `tan[tan^-1 ((2 cos x)/(sin^2 x))]` = 2 cosec x
⇒ `(2 cos x)/(sin^2 x)` = 2 cosec x
⇒ cos x = sin x
⇒ tan x = 1
⇒ x = tan−1 1
⇒ x = `pi/4`
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