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

Question

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

KnowledgeBoat · Accepted Answer

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

Mathematics

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

Trigonometric Identities

Related Questions

Prove the following identity:
sec² A + cosec² A = sec² A cosec² A

Prove the following identity:
tan² A + cot² A + 2 = sec² A cosec² A

Mathematics

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

Trigonometric Identities

Related Questions

Prove the following identity:sec2 A + cosec2 A = sec2 A cosec2 A

Prove the following identity:tan2 A + cot2 A + 2 = sec2 A cosec2 A

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

Prove the following identity:
sec² A + cosec² A = sec² A cosec² A

Prove the following identity:
tan² A + cot² A + 2 = sec² A cosec² A