Question

Prove the following trigonometric identities. $(sec^{2}\Theta-1)(cosec^{2}\Theta-1)=1$

Answer 1

Answer with Step-by-step explanation:

Given :  (sec²θ − 1)(cosec²θ - 1) = 1

L.H S :  (sec²θ − 1)(cosec²θ - 1)

= tan²θ × cot²θ

[By using the identity ,(sec²θ − tan²θ) = 1 & (cosec²θ− cot²θ) =1]

=(tanθ × cot θ)²

= (tanθ ×1/tanθ)²

[By using the identity ,cot θ = 1/tanθ ]

= 1²

= 1

(sec²θ − 1)(cosec²θ - 1) = 1

L.H.S = R.H.S  

Hence Proved..

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Answer 2

Refer the attachment.