Question

Please show all work. Show the steps in transforming the expression on the right into the one on the left. (Verifying identities - this is precalc.)

(1+3cosx-4cos²x)/sin²x = (1-4cosx)/(1-cosx)

Answer 1

(1 – 3cosx – 4cos^2x) / sin^2x =

(1+cos x)(1-4cos x) /(1-cos^2 x) =

(1+cos x)(1-4cos x) /[(1-cos x)(1+cos x)] =

(1-4cos x) /(1-cos x)
Factor:

1+cos(x))(1 – 4cos(x)) / (1 + cos(x))(1 – cos(x)) =

RHSCancel:(1 – 4cos(x)) / (1 – cos(x)) = RHSQED