Question 54

If $$\tan 4 \theta = \cot (2\theta + 30^\circ)$$, then $$\theta$$ is equal to:

Solution

Given that,

$$\tan 4 \theta = \cot (2\theta + 30^\circ)$$

We know that $$\cot (90-A)=\tan A$$

Hence,

$$\Rightarrow \cot(90^\circ-4\theta)=\cot (2\theta +30^\circ)$$

$$\Rightarrow 90^\circ -4\theta=2\theta + 30^\circ$$

$$\Rightarrow 6\theta=90^\circ -30^\circ$$

$$\Rightarrow \theta=\dfrac{60^\circ}{6}=10^\circ$$

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