Question

Prove that : (1 + cot^2theta)(1-costheta)(1+costheta)=1

Answer 1

Step-by-step explanation:

LHS

(1+cot²theta)(1-cos theta)(1+cos theta)

Now 1+cot²theta= cosec²theta

(cosec²theta)(1)²-(cos theta)² [using a²-b²=(a+b)(a-b)]

(cosec theta=1/sin theta

So cosec²theta=1/sin²theta)

Therefore,

(1/sin²theta)*1- cos²theta

(1/sin²theta)*sin²theta(since sin²theta+cos²theta=1)

sin²theta gets cancelled.

Therefore

LHS =1

LHS=RHS (Proved)

Hope this helps!!!