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प्रश्न
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
Prove that:
(cosec A − sin A) (sec A – cos A) (tan A + cot A) = 1
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उत्तर
L.H.S. = (cosec A – sin A) (sec A – cos A) (tan A + cot A)
= `(1/sinA - sinA)(1/cosA - cosA)(1/tanA + tanA)`
= `((1 - sin^2A)/sinA)((1 - cos^2A)/cosA)(sinA/cosA + cosA/sinA)`
= `(cos^2A/sinA)(sin^2A/cosA)((sin^2A + cos^2A)/(sinA.cosA))`
= `(cos^2A/sinA)(sin^2A/cosA)((1)/(sinA.cosA))`
= `(cos^2A sin^2A)/((sinA .cosA)(sinA.cosA ))`
= `(cos^2A sin^2A)/(sin^2A cos^2A)`
= 1
= R.H.S.
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