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