(1 – 3cosx – 4cos^2x) / sin^2x = (1 – 4cosx)/ (1 – cosx)?

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

Leave a Comment