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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
संबंधित प्रश्न
Prove the following identities:
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`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that a2 + b2 = m2 + n2
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Prove the following identities:
cosec4 A – cosec2 A = cot4 A + cot2 A
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`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove the following identities.
`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ
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