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प्रश्न
`(1+ cos theta)(1- costheta )(1+cos^2 theta)=1`
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उत्तर
LHS = `(1+costheta )(1-cos theta)(1+ cot^2 theta)`
=` (1-cos^2 theta) cosec^2 theta`
=` sin^2 theta xx cosec^2 theta`
=` sin^2 theta xx1/(sin^2 theta)`
=1
= RHS
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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
