Question

Prove identity: sin2x-tanx=cos2xtanx ​

Answer 1

See below.

Explanation:

sin2x-tanx

= 2sinx cosx - sinx/cos

= (2sinx cos^2x - sin x) / cos x

= sinx ( 2 cos^2x - 1 ) / cos x

Now sin x / cos x = tanx and 2 cos^2 x - 1 = cos2x

so this simplifies to cos2x tan x.