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सिद्ध कीजिए कि: 1 + (cot^2 α)/(1 + "cosec"  α) = "cosec"  α

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Question

सिद्ध कीजिए कि:

`1 + (cot^2 α)/(1 + "cosec"  α) = "cosec"  α`

Theorem
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Solution

बायाँ पक्ष = `1 + (cot^2 α)/(1 + "cosec"  α)`

= `1 + ("cosec"^2α - 1)/(1 + "cosec"  α)`

= `1 + ((1 + "cosec"  α)("cosec"  α - 1))/(1 + "cosec"  α)`

= 1 + cosec α – 1

= cosec α

= दायाँ पक्ष

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