Write the word or phrase that best completes each statement

Write the word or phrase that best completes each statement or answer Establish the identity. (sin x) (tan x cos x - cot x cos x) = 1 - 2 cos^2 x

12. sinx(tanx cos x - cotx cosx) =1-2cos²x

Starting with the left side

sinx(tanx cos x- cotx cos x)

using tanx =sinx/cos x and cot x=cos x/sin x

sinx(cos x(sin x/cos x)- (cos x/sin x)cosx)

sinx(sinx - cos²x/sinx)

Distributing sinx

sin²x - cos²x

1-cos²x - cos²x = 1-2cos²x which is equal to right side