Question

State true or false.

$\tan {69}^{\circ }+\tan {66}^{\circ }+1=\tan {69}^{\circ }\tan {66}^{\circ }$

• A. True
• B. False

Answer 1

The correct option is A True

$\tan {135}^{\circ }=\tan ({69}^{\circ }+{66}^{\circ })$

$\Rightarrow \tan ({180}^{\circ }-{45}^{\circ })=\frac{\tan {69}^{\circ }+\tan {66}^{\circ }}{1-\tan {69}^{\circ }\tan {66}^{\circ }}$

$\Rightarrow -\tan {45}^{\circ }=\frac{\tan {69}^{\circ }+\tan {66}^{\circ }}{1-\tan {69}^{\circ }\tan {66}^{\circ }}$

$\Rightarrow -1=\frac{\tan {69}^{\circ }+\tan {66}^{\circ }}{1-\tan {69}^{\circ }\tan {66}^{\circ }}$

$\Rightarrow -1+\tan {69}^{\circ }\tan {66}^{\circ }=\tan {69}^{\circ }+\tan {66}^{\circ }$

$\therefore \tan {69}^{\circ }+\tan {66}^{\circ }+1=\tan {69}^{\circ }\tan {66}^{\circ }$

Hence the given statement is true.