Question

How do you prove this identity?

cos2x*tan(π\4-x)= 1-sin2x

Answer 1

tan(π/4 - x) = (tanπ/4 - tanx)/(1 + tanπ/4 tanx)
= (1-tanx)/(1+tanx)
= (cosx-sinx)/(cosx+sinx)

see what you can do with that.