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QUESTION :- ( sin A + cosec A )² + ( cos A + sec A )² = 7 + tan²A + cot²A


ANSWER =

Taking L.H.S.

= ( sin A + cosec )² + ( cos A + sec A )²

= sin²A + cosec²A + 2 sin A cosec A + cos²A + sec²A + 2 cos A sec A

[ As we know that sin²A + cos²A = 1

sec²A = 1 + tan²A

cosec²A = 1 + cot²A ]

By applying the above formula we get,

= 1 + 1 + tan²A +1 + cot²A + 2 sin A cosec A + 2 cos A sec A

[ cosec A = 1/sin A and cos A = 1/sec A ]

By applying above formula we get,

= 1 + 1 + tan²A + 1 + cot² A + 2 sin A / sin A + 2 cos A / cos A

= 1 + 1 + tan² A + 1 + cot² A + 2 + 2

= 7 + tan²A + cot²A

L.H.S = R.H.S

Hence proved.

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