Question

ove that (cos? A - 1) (cot? A + 1) = -1
121​

Answer 1

Given:

• A trignometric equⁿ is given.
• The given expression is (cos²∅-1)(cot²∅+1)=-1.

To Prove:

• LHS = RHS.

Proof:

LHS = (cos²∅-1)(cot²∅+1)

= -1(1-cos²∅)(1+cot²∅)

= (-1) × sin²∅ × cosec²∅

= (-1) × sin²∅ × 1/sin²∅

= (-1)×1

= -1 = RHS

Hence proved