How do you prove (1 - sin2x) /(cos2x) = (cos2x) / (1 + sin2x)?
1 Answer
We have to prove that
To do this we transform left side:
(1-sin2x)/(cos2x)=((sin^2x+cos^2x)-2sinxcosx)/(cos2x)
=(sin^2x-2sinxcosx+cos^2x)/(cos^2x-sin^2x)
=(sinx-cosx)^2/((cosx-sinx)(cosx+sinx))
=((sinx-cosx)^2)/(-(sinx-cosx)(sinx+cosx))
=(cosx-sinx)/(cosx+sinx)
Now we expand the expresion by multiplying both numerator and denominator by
So we get:
((cosx-sinx)(cosx+sinx))/((cosx+sinx)^2)
=(cos^2x-sin^2x)/(cos^2x+2cosxsinx+sin^2x)
=(cos2x)/(1+sin2x)