Trigonometry questions

Question

Prove that 1-cos2x-sinx÷sin2x-cosx=tanx

Answer 1

1-cos^2(x) -(-sin^2(x)) - sinx all over 2sinxcosx - cosx = sinx/cosx

after substituting sin2x = 2sinxcosx, cos2x = cos^2(x) - sin^2(x), tanx=sinx/cosx

then substitute cos^2(s)+ sin^2(x) for 1 to get

2sin^2(x) -sinx over cosx(2sinx - 1) = sinx/cos2

divide by sinx or cancel the sinx on each side

cancel the 2sinx-1 on the left side's numerator & denominator

(sinx)(2sinx -1) all over cosx(2sinx-1) = sinx/cosx

cancel the sinx and 2sinx-1 to get

1/cosx = 1/cosx

multiply both sides by cosx

1 = 1

QED

Answer 2

Use x=30. See what happens.