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प्रश्न
Prove that `cosA/(1+sinA) + tan A = secA`
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उत्तर
L.H.S `cosA/(1+sinA) + tan A`
`= (cos A(1-sinA))/((1+sinA)(1-sinA)) + sinA/cosA`
`= (cosA - sinAcosA)/(1-sin^2A) + sinA/cosA`
`= (cosA - sinAcosA)/cos^2A + sinA/cosA`
`= 1/cosA - sinA/cosA + sinA/cosA`
`= 1/cosA`
= secA
=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
