Question

Prove that: [sin 4 theta - cos 4 theta + 1]cosec 2 theta=2

Answer 1

(sin⁴θ-cos⁴θ+1)cosec²θ
=[{(sin²θ)²-(cos²θ)²}+1]cosec²θ
=[{(sin²θ+cos²θ)(sin²θ-cos²θ)}+1]cosec²θ
=(sin²θ-cos²θ+1)cosec²θ [∵, sin²θ+cos²θ=1]
={sin²θ+(1-cos²θ)}cosec²θ
=(sin²θ+sin²θ)cosec²θ
=2sin²θ.cosec²θ
=2sin²θ×1/sin²θ
=2 (Proved)

Answer 2

Hi the above pinned image gives you the ans for your question