Question 70

If $$\tan x = \cot(45^\circ+ 2x)$$, then what is value of x?

Solution

Given,

$$\tan x = \cot(45^\circ+ 2x)$$

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

$$\Rightarrow \tan x = \tan(90^\circ-45^\circ- 2x)$$

$$\Rightarrow \tan x = \tan(45^\circ- 2x)$$

$$\Rightarrow x = 45^\circ- 2x$$

$$\Rightarrow 3x = 45^\circ$$

$$\Rightarrow x = 15^\circ$$

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