(cosec A - sin A)(sec A - cos A)sec² A = tan A.

Question

KnowledgeBoat · Accepted Answer

L.H.S. of the equation can be written as, As 1 - sin² A = cos² A and 1 - cos² A = sin² A. Dividing numerator and denominator by sin A cos A. Since, L.H.S. = R.H.S. hence proved that, (cosec A - sin A)(sec A - cos A)sec² A = tan A.

Mathematics

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:
(cosec A - sin A)(sec A - cos A)sec² A = tan A.

Trigonometric Identities

Related Questions

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:
(sin θ + cos θ)(sec θ + cosec θ) = 2 + sec θ cosec θ.

Mathematics

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:(cosec A - sin A)(sec A - cos A)sec2 A = tan A.

Trigonometric Identities

Related Questions

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:(sin θ + cos θ)(sec θ + cosec θ) = 2 + sec θ cosec θ.

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:
(cosec A - sin A)(sec A - cos A)sec² A = tan A.

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:
(sin θ + cos θ)(sec θ + cosec θ) = 2 + sec θ cosec θ.