How do I get the first part to equal the second part of the problem without changing the part after the equals sign?

### 2 Answers

(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)

You can change both sides, you just can’t cross the equals sign. That aside, you don’t need to change the right in this case, factor the numerator like a quadratic:

(1 + cos(x))(1 – 4cos(x)) / sin²(x) = RHS

Use the pythagorean theorem to change sin²(x):

(1+cos(x))(1-4cos(x)) / (1 – cos²(x)) = RHS

Factor:

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

Cancel:

(1 – 4cos(x)) / (1 – cos(x)) = RHS

QED