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