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Question
secθ + tanθ = `cosθ/(1 - sinθ)`
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Solution
डावी बाजू = secθ + tanθ
= `1/cosθ + sinθ/cosθ`
= `(1 + sinθ)/cosθ`
= `(1 + sinθ)/(cosθ) xx (1 - sinθ)/(1 - sinθ)` ....[अंशाचे परिमेयकरण करून]
= `(1^2 - sin^2θ)/(cosθ(1 - sinθ)) = (1 - sin^2θ)/(cosθ(1 - sinθ))`
= `(cos^2θ)/(cosθ(1 - sinθ))` .....`[(∵ sin^2θ + cos^2θ = 1), (∴ 1 - sin^2θ = cos^2θ)]`
= `cosθ/(1 - sinθ)` = उजवी बाजू
∴ secθ + tanθ = `cosθ/(1 - sinθ)`
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सिद्ध करा:
cotθ + tanθ = cosecθ × secθ
उकल:
डावी बाजू = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
= उजवी बाजू
∴ cotθ + tanθ = cosecθ × secθ
