chung minh dang thuc

Question

(1+Sin2x)/Cos2x=Tan(pi/4+x)

Answer 1

I assume you want to prove that it is an identity.

LS = (sin^2 x + cos^2 x + 2sinxcosx)/(cos^2 x - sin^2 x)
= (sinx + cosx)^2 / )(cosx+sinx)(cosx-sinx))
= (sinx + cosx)/(cosx - sinx)

RS = (tan π/4 + tanx)/( 1 - (tan π/4)(tanx) )
= (1 + tanx)/(1 - tanx)
= (1 + sinx/cosx) / 1 - sinx/cosx)
multiply top and bottom by cosx

= (cosx + sinx)/(cosx - sinx)
= LS

thus it is proven