Mathematics

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

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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 = $\dfrac{1}{4}$

Taking square root of both the sides we get,

⇒ sin θ = $\sqrt{\dfrac{1}{4}}$

⇒ sin θ = $\dfrac{1}{2}$

∴ θ = 30°.

Hence, the value of θ = 30°.

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