Question

cosa /1-tan a + sin a/1-cos a= cos a+ sin a

Answer 1

Sol:
cos a / (1 - tan a) + sin a /(1 - cot a) = sin a + cos a
LHS = cos A / (1 - tan A) + sin a /(1 - cot a)
= cos a / (cos a - sin a) + sin a / (sin a - cos a)
= cos a / (cos a - sin a) - sin a / (cos a - sin a)
= (cos a - sin a) / (cos a - sin a)
= (cos a + sin a) (cos a - sin a) / (cos a - sin a)
= (cos a + sin a).
Hence proved.

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