Prove the identity 1 sin2 x tanx cosx sinx Note that each

Prove the identity. (1 - sin^2 x) tanx = cosx sinx Note that each statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the corresponding question mark.

Solution

( 1- sin^2 x ) tan x = cos x sin x

proving the legft hand side

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

so now we have

cos^2 x tan x

tan x = sin x / cos x

cos^2 x ( sin x / cos x )

= sin x cos x

which is right hand side

hence proved !