1+costheta/sintheta=1/csctheta+cottheta

Question

Prove that these are trionometric identites

Answer 1

Remember the identity is csc^2x-cot^2x = 1

Rght hand side of identity = 1/csctheta+cottheta

multiple with csctheta-cottheta/csctheta-cottheta to identity.

= (1/csctheta+cottheta)(csctheta-cottheta/csctheta-cottheta)

= (csctheta-cottheta)/(csctheta)^2-(cottheta)^2

=  (csctheta-cottheta)/csc^2theta-cot^2theta

= (csctheta-cottheta)/1

= csctheta-cottheta

= 1/sintheta-costheta/sintheta

= (1-costheta)/sintheta

= left hand side identity.