Prove the following identity:

Question

prove the following identity:

 

2sin^2(x)/sin2(x)+cot(x)=sec(x)csc(x)

Answer 1

2sin²x / sin(2x) + cotx = 2sin²x / (2sinxcosx) + cotx

 

                                  = sinx / cosx + cosx / sinx

 

                                  = (sin²x + cos²x) / (cosxsinx)

 

                                  = 1/(cosxsinx)

 

                                  = (1/cosx)(1/sinx) = secxcscx

 

 

 

 

Answer 2

I think you have a mistake in your problem because the first term would simplify to 2.