Verify this trig identity csc x tan x 1 tan2x cos xSoluti

Verify this trig identity.

(csc x tan x) / (1 + tan^2x) = cos x

Solution

using following identity to simplify the left hand side

1+tan^2 x = sec^2 x

tan x = sin x / cos x

csc x = 1 / sin x

therefore, we have

(csc x tan x ) / ( sec ^2 x ) = ( 1/ sin x) ( sin x / cos x) / ( 1/ cos^2x)

= cos^2 x / cos x = cos x

cos x = cos x

hence proved