Question

(sin α + cosα)(tanα +cotα)=sec α + cosec α

Answer 1

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Answer 2

L. H. S.
( Sin a + cos a ) ( tan a + cot a) = ( sin a + cos a) ( sin a / cos a + cos a / sin a)
= ( sin a + cos a) ( sin ^2 a + cos ^2 a / sin a * cos a).
= ( sin a + cos a) ( 1 / sin a * cos a)
= ( sin a + cos a) /sin a * cos a
= (sin a / sin a * cos a) +(cos a / sin a* cos a)
= ( 1 / cos a) + ( 1 / sin a)
= sec a + cosec A = R. H. S.
Hence, Proved.