Verify the identity Simplify at each step 6 cos x 6 cos x1

Verify the identity. (Simplify at each step.) 6 cos x - 6 cos x/1 - tan x = 6 sin x cos x/sin x - cos x 6 cos x - 6 cos x/1 - tan x =

Solution

6cos x - (6 cos x/(1 - tan x)) = [(6 cos x*(1 - tan x)) - 6 cos x]/(1 - tan x)

= -6 cos x (tan x)/(1 - tan x) = [-6 cos x (sin x/cos x)/(1 - sin x/cos x)]*(cos x/cos x)

= -6cos x*sinx/(cos x - sin x) = 6cos x*sinx/(sin x - cos x)