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प्रश्न
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
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उत्तर
LHS = `cosec^4A - cosec^2A`
= `cosec^2A(cosec^2A - 1)`
RHS = `cot^4A + cot^2A`
= `cot^2A(cot^2A + 1)`
= `(cosec^2A - 1)cosec^2A`
Thus , LHS = RHS
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Show that, cotθ + tanθ = cosecθ × secθ
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
