Question

$\tan {180}^{\circ }$ + $\tan {125}^{\circ }$ + $\tan {100}^{\circ }$ . $\tan {125}^{\circ }$ is equal to

• A. -1
• B. 0
• C. 1/2
• D. 1

Answer 1

The correct option is D 1

We know,

$\tan ({180}^{\circ }+\theta )=\tan \theta$

$\Rightarrow$ tan (180° + 45°) = tan 45°

$\Rightarrow$ tan 225° = tan 45°

$\Rightarrow$ tan(100° + 125°) = tan 45°

$\Rightarrow \frac{\tan {100}^{\circ }+\tan {125}^{\circ }}{1-\tan {100}^{\circ }\tan {125}^{\circ }}=\tan {45}^{\circ }$ Using $\left[\tan \right(x+y)=\frac{\tan x+\tan y}{1-\tan x\tan y}]$

$\Rightarrow \tan {100}^{\circ }+\tan {125}^{\circ }=1-\tan {100}^{\circ }+\tan {125}^{\circ }$

$\Rightarrow \tan {100}^{\circ }+\tan {125}^{\circ }+\tan {100}^{\circ }\tan {125}^{\circ }=1$

Hence, correct option is D.