If sin A + cosec A = 2; find the value of sin2 A + cosec2 A.

Question

KnowledgeBoat · Accepted Answer

sin A \+ cosec A = 2 Squaring both sides, (sin A \+ cosec A)2 = 22 ⇒ sin2 A \+ cosec2 A \+ 2 x sin A x cosec A = 4 ⇒ sin2 A \+ cosec2 A \+ 2 x sin A x = 4 ⇒ sin2 A \+ cosec2 A \+ 2 x x = 4 ⇒ sin2 A \+ cosec2 A \+ 2 = 4 ⇒ sin2 A \+ cosec2 A = 4 \- 2 ⇒ sin2 A \+ cosec2 A = 2 Hence, sin2 A + cosec2 A = 2.

Mathematics

If sin A + cosec A = 2; find the value of sin² A + cosec² A.

Trigonometric Identities

Related Questions

Using the measurements given in the following figure :
(i) Find the value of sin Φ and tan θ.
(ii) Write an expression for AD in terms of θ.

If tan A + cot A = 5; find the value of tan² A + cot² A.

Given : 4 sin θ = 3 cos θ; find the value of :
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Mathematics

If sin A + cosec A = 2; find the value of sin2 A + cosec2 A.

Trigonometric Identities

Related Questions

Using the measurements given in the following figure :(i) Find the value of sin Φ and tan θ.(ii) Write an expression for AD in terms of θ.

If tan A + cot A = 5; find the value of tan2 A + cot2 A.

Given : 4 sin θ = 3 cos θ; find the value of :(i) sin θ(ii) cos θ(iii) cot2 θ - cosec2 θ(iv) 4 cos2 θ - 3 sin2 θ + 2

If sin A + cosec A = 2; find the value of sin² A + cosec² A.

Using the measurements given in the following figure :
(i) Find the value of sin Φ and tan θ.
(ii) Write an expression for AD in terms of θ.

If tan A + cot A = 5; find the value of tan² A + cot² A.

Given : 4 sin θ = 3 cos θ; find the value of :
(i) sin θ
(ii) cos θ
(iii) cot² θ - cosec² θ
(iv) 4 cos² θ - 3 sin² θ + 2