If θ is positive acute angle and 7 cos²θ

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If θ is positive acute angle and 7 cos²θ + 3 sin²θ = 4, then the value of θ is :

7 cos²θ + 3 sin²θ = 4
⇒ 7 (1 – sin²θ) + 3 sin²θ = 4
⇒ 7 – 7 sin²θ + 3sin²θ = 4
⇒ 7 – 4 sin²θ = 4
⇒ 4 sin²θ = 7 – 4 = 3

⇒ sin²θ =	3
	4

⇒ sinθ =	√3
	2

∵0 < q < 90°
⇒ θ = 60°