Prove that: (tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1 - Mathematics

Prove that:

(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1

Sum

(tan A + cot A) (cosec A – sin A) (sec A – cos A)

= `(sinA/cosA + cosA/sinA)(1/sinA - sinA)(1/cosA - cosA)`

= `((sin^2A + cos^2A)/(sinAcosA))((1 - sin^2A)/sinA)((1 - cos^2A)/cosA)`

= `(1/(sinAcosA))(cos^2A/sinA)(sin^2A/cosA)`

= 1

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