Prove the following identities : (sin A + cosec A)^2 + (cos A + sec A)^2 = 7 + tan^2 A + cot^2 A

By formula, sin 2 A + cos 2 A = 1 sec 2 A = 1 + tan 2 A cosec 2 A = 1 + cot 2 A Solving L.H.S. of the equation : ⇒ (sin A + cosec A) 2 + (cos A + sec A) 2 = 7 + tan 2 A + cot 2 A ⇒ sin 2 A + cosec 2 A + 2 sin A. cosec A + cos 2 A + sec 2 A + 2 cos A. sec A ⇒ sin 2 A + 1 + cot 2 A + 2 × sin A × + cos 2 A + 1 + tan 2 A + 2 × cos A × ⇒ sin 2 A + cos 2 A + 1 + cot 2 A + 2 + 1 + tan 2 A + 2 ⇒ 1 + 1 + 2 + 1 + 2 + cot 2 A + tan 2 A ⇒ 7 + tan 2 A + cot 2 A. Since, L.H.S. = R.H.S. Hence, proved that (sin A + cosec A) 2 + (cos A + sec A) 2 = 7 + tan 2 A + cot 2 A.

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

View Answer Bookmark Now

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

View Answer Bookmark Now

Mathematics

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

Trigonometric Identities

Related Questions

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

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

Mathematics

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

Trigonometric Identities

Related Questions

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

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

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

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

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