Prove the following identity:
(sin A + cosec A)² + (cos A + sec A)² = 7 + tan² A + cot² A

Question

Prove the following identity: (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A

KnowledgeBoat · Accepted Answer

By formula, sin2 A + cos2 A = 1 sec2 A = 1 + tan2 A cosec2 A = 1 + cot2 A Solving L.H.S. of the equation : ⇒ (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A ⇒ sin2 A + cosec2 A + 2 sin A. cosec A + cos2 A + sec2 A + 2 cos A. sec A ⇒ sin2 A + 1 + cot2 A + 2 × sin A × + cos2 A + 1 + tan2 A + 2 × cos A × ⇒ sin2 A + cos2 A + 1 + cot2 A + 2 + 1 + tan2 A + 2 ⇒ 1 + 1 + 2 + 1 + 2 + cot2 A + tan2 A ⇒ 7 + tan2 A + cot2 A. Since, L.H.S. = R.H.S. Hence, proved that (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A.

Mathematics

Prove the following identity:
(sin A + cosec A)² + (cos A + sec A)² = 7 + tan² A + cot² A

Trigonometric Identities

Answer

Related Questions

Prove the following identity:
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(1 + cot A - cosec A)(1 + tan A + sec A) = 2

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$\Big(\dfrac{\tan A}{1 - \cot A}\Big) + \Big(\dfrac{\cot A}{1 - \tan A}\Big) = \sec A \cosec A + 1$

Mathematics

Prove the following identity:(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A

Trigonometric Identities

Answer

Related Questions

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Prove the following identity:
(sin A + cosec A)² + (cos A + sec A)² = 7 + tan² A + cot² A

Prove the following identity:
$\Big(\dfrac{\cosec A}{\cosec A - 1}\Big) + \Big(\dfrac{\cosec A}{\cosec A + 1}\Big) = 2 \sec^2 A$

Prove the following identity:
(1 + cot A - cosec A)(1 + tan A + sec A) = 2

Prove the following identity:
$\Big(\dfrac{\cos^3 A + \sin^3 A}{\cos A + \sin A}\Big) + \Big(\dfrac{\cos^3 A - \sin^3 A}{\cos A - \sin A}\Big) = 2$

Prove the following identity:
$\Big(\dfrac{\tan A}{1 - \cot A}\Big) + \Big(\dfrac{\cot A}{1 - \tan A}\Big) = \sec A \cosec A + 1$