If 7 sin² θ + 3 cos² θ = 4, 0° ≤ θ ≤ 90°, then find the value of θ.

Question

KnowledgeBoat · Accepted Answer

Given, ⇒ 7 sin² θ + 3 cos² θ = 4 ⇒ 4 sin² θ + 3 sin² θ + 3 cos² θ = 4 ⇒ 4 sin² θ + 3(sin² θ + cos² θ) = 4 ⇒ 4 sin² θ + 3 = 4 ⇒ 4 sin² θ = 4 - 3 ⇒ 4 sin² θ = 1 ⇒ sin² θ = Taking square root of both the sides we get, ⇒ sin θ = ⇒ sin θ = ∴ θ = 30°. Hence, the value of θ = 30°.

Mathematics

If 7 sin² θ + 3 cos² θ = 4, 0° ≤ θ ≤ 90°, then find the value of θ.

Trigonometric Identities

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