Question

prove the identity (sin(2x)/sinx)-(cos(2x)/cosx)=secx

Answer 1

= 2 sinx cosx 2 cos^2 x - 1
---------- - ------------
sin x cos x

= 2 cos x - 2 cos x + 1 + 1 / cos x
= sec x

Answer 2

* second line should be

= 2 cos x - 2 cos x + 1 / cos x

Answer 3

2sinxcosx/sinx - cos^2x-sin^2x/cosx

2cosx-(cos^2x-1+cos^2x)/cosx

2cos^2x-Cos^2x+1-Cos^2x/cosx

1/cosx=Secx