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प्रश्न
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
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उत्तर
LHS = `(1 - tan^2 θ)/(cot^2 θ - 1)`
= `(1 - tan^2 θ)/(1/tan^2 θ - 1)`
= `((1 - tan^2 θ)/(1 - tan^2 θ)/tan^2 θ) `
= tan2 θ
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities
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`5/(sin^2θ) - 5cot^2θ`, complete the activity given below.
Activity:
`5/(sin^2θ) - 5cot^2θ`
= `square (1/(sin^2θ) - cot^2θ)`
= `5(square - cot^2θ) ...[1/(sin^2θ) = square]`
= 5(1)
= `square`
