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प्रश्न
What is the value of \[\sin^2 \theta + \frac{1}{1 + \tan^2 \theta}\]
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उत्तर
We have,
`sin^2 θ+1/(1+tan^2θ)= sin^2θ+1/(sqc^2θ)`
=` sin^2θ+(1/secθ)^2`
=` sin^2 θ+cos^2θ`
=` 1`
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Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
