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प्रश्न
Find the value of x for which (sin A + cosec A)2 + (cos A + sec A)2 = x + tan2 A + cot2 A.
योग
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उत्तर
(sin A + cosec A)2 + (cos A + sec A)2 = x + tan2 A + cot2 A
L.H.S. = sin2 A + cosec2 A + 2 sin A cosec A + cos2 A + sec2 A + 2 cos A sec A
= `(sin^2 A + cos^2 A) + (1 + cot^2 A) + 2 sin A xx 1/(sin A) + (1 + tan^2 A) + 2 cos A. 1/(cos A)`
= 1 + 1 + cot2 A + 2 + 1 + tan2 A + 2
= 7 + cot2 A + tan2 A
∴ x = 7
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