Question

Verify the following identity : (sinx+cosx)^2/sin2x=csc2x+1?

Please help

Answer 1

We have:

`(sinx + cosx)^2/(sin(2x)) = csc(2x) + 1`

`(sin^2x +cos^2x + 2sinxcosx)/(2sinxcosx) = csc(2x) + 1`

`(1+ 2sinxcosx)/(2sinxcosx)= csc(2x) +1`

`1/(2sinxcosx) + 1 = csc(2x) + 1`

`1/sin(2x) + 1 = csc(2x) +1`

`csc(2x) +1 = csc(2x) + 1`

`LHS = RHS`

As required.

Hopefully this helps!