Question

prove Cosec^2theta = 1+Cos^2theta
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Answer 1

To prove

cosec²∅ = 1 + cot²∅

Proof

We know that cosec∅ = H/P (H being the hypotenuse and P being the perpendicular)

and cot∅ = B/P (B being the base and P being the perpendicular)

Now, 1 + cot²∅ = 1 + (B/P)²

⇒ 1 + B²/P²

⇒ P²/P² + B²/P²

⇒ (P² + B²)/P²

⇒ H²/P² (By Pythagoras Theorem, we have H² = P² + B²)

⇒ (H/P)²

⇒ (cosec∅)² (since, cosec∅ = H/P)

⇒ cosec²∅

Hence, 1 + cot²∅ = cosec²∅