Question

Prove the following trigonometric identities. $\frac{(1+tan^{2}\Theta)cot\Theta }{cosec^{2}\Theta } =tan\Theta$

Answer 1

Answer with Step-by-step explanation:

Given :  

(1 + tan²θ)cotθ/(cosec²θ) = tanθ

 

LHS = (1 + tan²θ)cotθ/(cosec²θ)  

= sec²θ cotθ/(cosec²θ)

[By using  an identity, (1 + tan²θ) = sec²θ]

= sec²θ × cotθ × 1/(cosec²θ)

= 1/cos²θ × cosθ/sinθ  × sin²θ

[By using an identity, secθ = 1/cosθ, cosecθ = 1/sinθ,cotθ = cosθ/sinθ]

= sinθ/cosθ

= tanθ

[By using the identity, tanθ = sinθ/cosθ ]

(1 + tan²θ)cotθ/(cosec²θ) = tanθ

L.H.S = R.H.S  

Hence Proved..

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Answer 2

Answer:

Refer to the attachment for your answer.