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प्रश्न
Prove the following trigonometric identities.
(cosecA − sinA) (secA − cosA) (tanA + cotA) = 1
उत्तर
We have to prove (cosecA − sinA) (secA − cosA) (tanA + cotA) = 1
We know that `sin^2 A + cos^2 A = 1`
So
(cosec A - sin A)(sec A - cos A)(tan A + cot A)
`= (1/sin A - sin A)(1/cos A - cos A)(sin A/cos A + cos A/sin A)`
`= ((1 - sin^2 A)/sin A) ((1 - cos^2 A)/cos A) (sin^2 A + cos^2 A)/(sin A cos A)`
`= ((cos^2 A)/sin A) ((sin^2 A)/cos A) (1/(sin A cos A))`
`(= sin^2 A cos^2 A)/(sin^2 A cos^2 A)`
= 1
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