Question

cot^2 θ - 1/sin^2 θ = ?

Answer 1

cot² θ - 1/ sin² θ = - cosec²θ / sin²θ
= - 1/ sin²θ ÷ sin²θ
= - 1 × sin²θ × sin²θ
= - 1
Therefore, - 1 is the required answer.

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Answer 2

we know that 1/sin^2 theta =cosec^2theta

cot^2theta-cosec^2theta=1