Question

Prove the following trigonometric identities. $tan\Theta+\frac{1}{tan\Theta}=sec\Theta cosec\Theta$

Answer 1

Answer with Step-by-step explanation:

Given : tan θ + 1/tan θ = sec θ cosec θ

L.H.S :   tan θ + 1/tan θ

= (tan²θ +1) /tanθ

= sec²θ/ tanθ

[By using the identity ,1 +  tan²θ = sec²θ]

= secθ [(secθ/ tanθ)]

= secθ [(1/cosθ)/(sinθ/cosθ)]

= secθ [1/cosθ × cosθ/sinθ]

= secθ 1/sinθ

= secθ cosecθ

[By using the identity ,1/Sin A = Cosec A]

tan θ + 1/tan θ = sec θ cosecθ

L.H.S = R.H.S  

Hence Proved..

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Answer 2

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