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hey mate,
here is your answer,
(viii) (sin A +cosec A) ² + (cos A +sec A)² =7+tan A ² + cot A ²
squaring on both sides, we get
sin² A + cosec² A + 2 × sin A × cosecA + cos² A + sec² A + 2 secA × cosA
as we know we can write,
cosec² A = 1 + cot² A
sec² A = 1+ tan² A
sin² A+ cos² A = 1
sin A × cosec A = 1 = sec A×cos A
hence ,
=1 + 1 + cot² A + 2 + 1 + tan² A + 2
=7 + tan² A + cot² A
=R.H.S.
hence proved.
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