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प्रश्न
Prove the following trigonometric identities.
tan2 θ − sin2 θ = tan2 θ sin2 θ
Prove that:
tan2 θ − sin2 θ = tan2 θ sin2 θ
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उत्तर
LHS = tan2 θ − sin2 θ
= `sin^2 θ/cos^2 θ - sin^2 θ` `[∵ tan^2 θ = sin^2 θ/cos^2 θ]`
`=> sin^2 θ [1/cos^2 θ- 1]`
`sin^2 θ [(1 - cos^2 θ)/cos^2 θ]`
`=> sin^2 θ. sin^2 θ/cos^2 θ = sin^2 θ tan^2 θ `
LHS = RHS
Hence proved
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