Verify the identity?

Question

#(1+sin 2x)/(cos 2x) = (cos x + sin x)/(cos x - sin x)#

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Answer 1 · 2018-05-07T01:03:07

Using:
#sin2x= 2sinxcosx#
#cos2x= cos^2x-sin^2x#
#sin^2x+cos^2x=1#

#(1+sin 2x)/(cos 2x) = (cos x + sin x)/(cos x - sin x)#

#(1+2sinxcosx)/(cos^2x-sin^2x)= (cos x + sin x)/(cos x - sin x)#

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

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

#((sinx+cosx)(sinx+cosx))/((cosx-sinx)(cosx+sinx))= (cos x + sin x)/(cos x - sin x)#

#(cancel((sinx+cosx))(sinx+cosx))/((cosx-sinx)cancel((cosx+sinx)))= (cos x + sin x)/(cos x - sin x)#

#(cos x + sin x)/(cos x - sin x)=(cos x + sin x)/(cos x - sin x)#