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प्रश्न
`(sec^2 theta -1)(cosec^2 theta - 1)=1`
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उत्तर
LHS = `(sec^2 theta -1)(cosec^2 theta-1)`
=`tan^2 theta xx cot^2 theta ( ∵ sec^2 theta - tan^2 theta = 1 and cosec^2 theta - cot^2 theta =1)`
=` tan^2 theta xx1/(cos^2theta)`
=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
