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प्रश्न
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
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उत्तर
L.H.S. = `cosA/(1-sinA)`
= `(cosA(1 + sinA))/((1 - sinA)(1 + sinA))`
= `(cosA(1 + sinA))/(1 - sin^2A)`
= `(cosA(1 + sinA))/(cos^2A)`
= `(1 + sinA)/cosA`
= `1/cosA + sinA/cosA`
= sec A + tan A = R.H.S.
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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
