If 3(\cot^2 \theta - \cos^2 \theta) = 1 - \sin^2 \theta, 0^\circ < \theta < 90^\circ, then the \theta equal to

Question 133

If $$3(\cot^2 \theta - \cos^2 \theta) = 1 - \sin^2 \theta, 0^\circ < \theta < 90^\circ$$, then the $$\theta$$ equal to

Solution

$$3(\cot^2 \theta - \cos^2 \theta) = 1 - \sin^2 \theta, 0^\circ < \theta < 90^\circ$$

$$\Rightarrow 3(\dfrac{\cos^2\theta}{\sin^2\theta} - \cos^2 \theta) = 1 - \sin^2 \theta$$

$$\Rightarrow 3\cos^2\theta(\dfrac{1-\sin^2\theta}{\sin^2\theta} ) = 1 - \sin^2 \theta$$

$$\Rightarrow \tan^2\theta=3$$

$$\Rightarrow \tan\theta=\sqrt{3}=\tan 60^\circ$$

$$\theta=60^\circ$$

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