Question

Prove the following trigonometric identities. $\frac{cos^{2}\Theta}{sin\Theta}-cosec\Theta+sin\Theta=0$

Answer 1

Answer with Step-by-step explanation:

Given : cos²θ/sinθ − cosec θ + sinθ = 0

L.H.S : cos²θ/sinθ − cosec θ + sinθ

= (cos²θ/sinθ − 1/sinθ) + sinθ

[By using the identity, cosecθ = 1/ sinθ]

= (cos²θ − 1)/sinθ + sinθ

= (− sin²θ ) /sinθ + sinθ

[By using the identity, (1- cos²θ) = sin²θ]

= −sinθ + sinθ

= 0

cos²θ/sinθ − cosec θ + sinθ = 0

L.H.S = R.H.S  

Hence Proved..

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Answer 2

Answer:

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