Question

Prove the identity of the following equation:
(cos 2x)/(1/(cos x)) * (sin(pi + x))/(tan x) = (sec(x) - csc(x)) * (csc(x))/(sec^2 x) * (1 - cos^2 x)

Show steps to accomplish the answers

Answer 1

take apart the LS
(cos 2x)/(1/(cos x)) is just (cos 2x)(cosx)
(sin(pi + x))/(tan x) = -sinx(cosx)/sinx = -cosx

so LS = (cos 2x)(cosx)*(-cosx)
= -(cos 2x)(cos^2 x)

RS = (sec(x) - csc(x)) * (csc(x))/(sec^2 x) * (1 - cos^2 x)
= (1/cosx - 1/sinx)*(cos^2 x)/sinx * (sin^2 x)
= (sinx - cosx)/(sinxcosx)*(cos^2 x)sinx
= (sinx - cosx)(cosx)

testing for x = 30°
LS = -.375
RS = -.316...

The equation is not an identity the way you typed it