Question

Solve $\frac{tan3x-tan2x}{1+tan3xtan2x}=1$.

• A. ${95}^{\circ }$
• B. ${45}^{\circ }$
• C. ${55}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

We have

$\frac{\tan 3x-\tan 2x}{1+\tan 3x\tan 2x}=1$

$\Rightarrow \tan (3x-2x)=1$

$\Rightarrow \tan x=\tan {45}^0$

$x={45}^0$

Hence, this is the answer.