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

Given: 4 sin θ = 3 cos θ ∴ If length of BC = 3x unit, length of AB = 4x unit. In Δ ABC, ⇒ AC2 = BC2 \+ AB2 (∵ AC is hypotenuse) ⇒ AC2 = (3x)2 \+ (4x)2 ⇒ AC2 = 9x2 \+ 16x2 ⇒ AC2 = 25x2 ⇒ AC = ⇒ AC = 5x (i) sin θ = Hence, sin θ = . (ii) cos θ = Hence, cos θ = . (iii) cot2 θ - cosec2 θ + 2 cot θ = cosec θ = Now, cot2 θ - cosec2 θ Hence, cot2 θ - cosec2 θ + 2 = -1. (iv) 4 cos2 θ - 3 sin2 θ + 2 cos θ = sin θ = Now, 4 cos2 θ - 3 sin2 θ + 2 Hence, 4 cos2 θ - 3 sin2 θ + 2 =.

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

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

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Given : 17 cos θ = 15; find the value of tan θ + 2 sec θ.

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Mathematics

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

Trigonometric Identities

Related Questions

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

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

Given : 17 cos θ = 15; find the value of tan θ + 2 sec θ.

Mathematics

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

Trigonometric Identities

Related Questions

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

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

Given : 17 cos θ = 15; find the value of tan θ + 2 sec θ.

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.

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