Question

Prove that they are equal

Answer 1

Explanation:

(1-tanx)/(1+tanx) = (1-sin2x)/cos2x

Replace tanx with sinx/cosx:

(1-sinx/cosx)/(1+sinx/cosx)

Multiply numerator and denominator by cosx:

(cosx-sinx)/(cosx+sinx)

Multiply numerator and denominator by cosx-sinx:

(cos^2x-2sinxcosx+sin^2x)/(cos^2x-sin^2x)

For the numerator, since sin2x = 2sinxcosx, and sin^2x + cos^2x = 1, we have 1-sin2x

For the denominator, cos^2x - sin^2x = cos2x

So (1-tanx)/(1+tanx) = (1-sin2x)/cos2x