Question

27. Prove that:
(sin4 0 - cos 4 0 + 1) cosec2 0 = 2


0 = theata
​

Answer 1

Answer:

(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)

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