Question

Prove that:

(1+ cot² A) (1 − cos A) (1 + cos A) = 1

Answer 1

Solving L.H.S. of the equation:

⇒ (1 + cot² A)(1 − cos A)(1 + cos A)

⇒ (1 + cot² A)(1 − cos² A)

By formula,

1 + cot² A = cosec² A and 1 − cos² A = sin² A.

⇒ cosec²A × sin²A

⇒ `1/(sin^2A) × sin^2A`

⇒ 1

Since, L.H.S. = R.H.S.