Question

Prove the following identities:

a) (cosec θ + cotθ)(cosecθ - cotθ) = cotθtanθ


b) 2/(1 + sinθ) + 1/(1- sinθ) = (3sec^2)θ - tanθcosecθ


I basically just have to prove Left HandSide = Right Hand Side

Answer 1

(a) You should immediately recognize that the right side equals 1. If you don't, then review the relationship of tan and cot.

Multiply out the two factors on the left and you get
csc^2 θ - cot^2 θ) = 1

Rewrite the left side as
1/ sin^2 - cos^2/sin^2 = 1
which is the same as
(1 - cos^2)/sin^2 = 1
1 = 1

For (b), I suggest first rewriting the left side with a common denominator. Also recognize that tan*csc on the right equals sec = 1/cos

Answer 2

Thanks drwls that really helped !
:)