If cot²θ-2 cos²θ=0, (0^°, then the value of θ is:

If $cot^2\theta-2 cos^2\theta=0, (0^\circ<\theta<90^\circ)$ , then the value of $\theta$ is:

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. $45^\circ$ .

$cot^2\theta-2 cos^2\theta=0$

⇒ cos²θ/sin²θ - 2cos²θ = 0

⇒ cos²θ(1/sin²θ - 2) = 0

⇒ 1/sin²θ - 2 = 0

⇒ 1/sin²θ = 2

⇒ sin²θ = 1/2

⇒ sinθ = 1/√2

⇒ sinθ = sin45°

⇒ θ = 45°

SSC CGL 2024 PYQ — Question 66