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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

Show that `Sqrt((1+Cosa)/(1-cosa)) = Cosec a + Cot A`

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प्रश्न

Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`

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उत्तर

L.H.S = `sqrt((1-cosA)/(1+cos A))`

`= sqrt((1-cosA)/(1+cosA) xx (1 - cos A)/(1- cos A)) = sqrt((1- cosA)^2/(1-cos^2A))`

`=sqrt((1- cosA)^2/(sin^2A)) = (1-cosA)/sin A = 1/sin A - cos A/sin A = cosec A -cot A` = R.H.S

Hence prove.

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2017-2018 (March) Set A

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