Question

Having trouble with trigonometry , please help.

CSCx (1 + SINx) = 1 + CSCx

prove the identity

Answer 1

Remember that the cosecant is the reciprocal of the sine. CSC(x) = 1/SIN(x).

Now operate on the left side, and see if you can make it look like the right side:

CSCx (1 + SINx)

Substitute for CSCx :

(1/SINx) (1 + SINx)

Multiply them:

1/SINx + SINx/SINx
which is the same as 1/SINx + 1
which is the same as CSCx + 1,
and that's the right side of the identity, so you proved it.