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प्रश्न
What is the value of (1 + tan2 θ) (1 − sin θ) (1 + sin θ)?
उत्तर
We have,
`(1+tan^2θ)(1-sinθ)(1+sin θ)=(1+tan ^2 θ){(1-sinθ)(1+sinθ)}`
= `(1+tan^2θ)(1-sin^2θ)`
We know that,
`sec^2θ-tan^2θ=1`
⇒ `sec^2 θ=1+tan^2θ`
`sin^2 θ+cos ^2θ=1`
⇒ `cos^2 θ=1sin^2θ`
Therefore,
`(1+tan^2θ)(1-sin θ)(1+sin θ) = sec^2 θ xxcos^2θ`
= `1/cos^2θ xx cos^2 θ`
=` 1`
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