Prove the identity tan pi x tan x Note that each Statement

Prove the identity. tan (pi - x)= -tan x Note that each Statement must be based on a Rule chosen from the Rule mark.

tan x ( 1+ cos 2x ) = sin 2x

cos 2x = cos^x - sin^2 x

sin 2x = 2 sin x cos x

tan x = sin x / cos x

sin x / cos x ( 1 + cos^-x - sin^2 x)

proving left hand side

sin x / cosx ( sin^2 x + cos^2 x + cos^2x - sin^2x )

sin x / cos x ( 2 cos^2 x )

2 sin x cos x = 2 sin x cos x or sin 2x

left hand side = right hand side

proved