Question

Cos a - sin +1÷cos a+sin a-1=cosec a+cot a, using the identity cosec sq a=1+cot sq a

Answer 1

cos a - sin a + 1

------------------------ = cosec a + cot a

cos a + sin a -1

L.H.S.

cos a /sin a - sin a / sin a + 1 / sin a

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cos a /sin a + sin a / sin a - 1 / sin a

cot a - cosec a + 1

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cot a + cosec a - 1

cot a + cosec a - (cot²a - cosec²a)

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cot a + cosec a - 1

cot a + cosec a - (cot a - cosec a)(cot a + cosec a)

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cot a + cosec a - 1

cot a + cosec a ( 1 - cot a + cosec a)

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-(1 - cot a + cosec a)

-cot a -cosec a