Prove the following identity:
(cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ) = 1

Question

Prove the following identity: (cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ) = 1

KnowledgeBoat · Accepted Answer

Solving L.H.S. of the equation : ⇒ (cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ) = 1 Since, L.H.S. = R.H.S. Hence, proved that (cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ) = 1.

Mathematics

Prove the following identity:
(cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ) = 1

Trigonometric Identities

Related Questions

Prove the following identity:
cosec A (1 + cos A)(cosec A - cot A) = 1

Prove the following identity:
sec A (1 - sin A)(sec A + tan A) = 1

Prove the following identity:
(cosec A + sin A)(cosec A - sin A) = cot² A + cos² A

Prove the following identity:
(sec A + cos A)(sec A - cos A) = sin² A + tan² A

Mathematics

Prove the following identity:(cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ) = 1

Trigonometric Identities

Related Questions

Prove the following identity:cosec A (1 + cos A)(cosec A - cot A) = 1

Prove the following identity:sec A (1 - sin A)(sec A + tan A) = 1

Prove the following identity:(cosec A + sin A)(cosec A - sin A) = cot2 A + cos2 A

Prove the following identity:(sec A + cos A)(sec A - cos A) = sin2 A + tan2 A

Prove the following identity:
(cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ) = 1

Prove the following identity:
cosec A (1 + cos A)(cosec A - cot A) = 1

Prove the following identity:
sec A (1 - sin A)(sec A + tan A) = 1

Prove the following identity:
(cosec A + sin A)(cosec A - sin A) = cot² A + cos² A

Prove the following identity:
(sec A + cos A)(sec A - cos A) = sin² A + tan² A