Question

cos²θ +1/1+ cot²θ =1,Prove it by using trigonometric identities.

Answer 1

Given :

cos²θ +1/1+ cot²θ =1

LHS = cos²θ +(1/1+ cot²θ)

= cos²θ +1/cosec²θ

[1+ cot² θ = cosec²θ]

= cos²θ + sin²θ = 1

[ 1/ cosecθ = sinθ ]

LHS = cos²θ + sin²θ = 1 = RHS

**Trigonometric identities : An equation involved in trigonometry ratios of an angle θ is said to be trigonometric identity if it is satisfied for all values of θ for which the given trigonometric ratios are defined.

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Answer 2

LHS = cos²θ + 1/( 1 + cot²θ )

=  cos² θ+ 1 / cosec²θ

[ ∵ 1+cot²θ = cosec²θ]

= cos²θ + sin²θ

[ ∵ 1/cosec²θ = sin²θ]

= 1

[∵ cos²θ + sin²θ= 1 ]

= RHS

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