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प्रश्न
Prove that `(cos(90^circ - A))/(sin A) = (sin(90^circ - A))/(cos A)`.
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उत्तर
L.H.S. = `(cos(90^circ - A))/(sin A)`
= `(sin A)/(sin A)`
= 1
R.H.S. = `(sin(90^circ - A))/(cos A)`
= `(cos A)/(cos A)`
= 1
∴ L.H.S. = R.H.S.
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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
