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प्रश्न
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
उत्तर
We know that,
`sin^2 A + cos^2 A = 1`
`sec^2 A - tan^2A = 1`
So
`sin^2 A + 1/(1 + tan^2 A) = sin^2 A + 1/sec^2 A`
`= sin^2 A + (1/sec A)^2`
`= sin^2 A + (cos A)^2`
`= sin^2 A + cos^2 A`
= 1
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