1 cos 2 x sin x tanx cos xSolution 1 cos2 x sin x 1 cos2

1 - cos ^2 x / sin x

tan(-x) cos (-x)

( 1- cos^2 x ) / sin x

(1- cos^2 x ) = sin^2 x (from the identity sin^2 x + cos^2 x = 1)

hence, expression becomes

sin^2 x / sin x = sin x

so, 1 - cos ^2 x / sin x = sin x

tan(-x) cos (-x)

tan (-x) = - tan x = - sin x / cos x

cos (-x) = cos x

hence,

tan(-x) cos (-x) = - sin x / cos x * cos x = - sin x