Question 61

If $$\tan 4\theta = \cot(40^\circ - 2\theta), then \theta$$ is equal to:

Solution

As per the question,

$$\tan 4\theta = \cot(40^\circ - 2\theta)$$

We know that $$\cot \theta=\tan(90^\circ- \theta)$$

So, $$\tan 4\theta = \tan(90^\circ -40^\circ + 2\theta)$$

$$\tan 4\theta = \tan(50^\circ + 2\theta)$$

Hence, $$4\theta =50^\circ +2 \theta$$

$$\Rightarrow 2\theta =50^\circ $$

$$\Rightarrow \theta =25^\circ $$

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: