Question

The value of $\frac{\cos {15}^o-\sin {15}^o}{\cos {15}^o+\sin {15}^o}$ is equal to

• A. $\frac{1}{\sqrt{3}}$
• B. $\sqrt{3}$
• C. $\frac{1}{2}$
• D. $1$

Answer 1

The correct option is A $\frac{1}{\sqrt{3}}$

$\frac{cos{15}^{\circ }-sin{15}^{\circ }}{cos{15}^{\circ }+sin{15}^{\circ }}$

$\Rightarrow \frac{1-tan{15}^{\circ }}{1+tan{15}^{\circ }}$

$\Rightarrow \frac{\left(tan{45}^{\circ }\right)-\left(tab{15}^{\circ }\right)}{1+\left(tan{45}^{\circ }\right)\left(tan{15}^{\circ }\right)}$

[(on dividing $cos{15}^{\circ }$ both side)

as $tan(x-y)=\frac{tanx-tany}{1+tanxtany}]$

$\Rightarrow tan({45}^{\circ }-{15}^{\circ })$

$\Rightarrow tan\left({30}^{\circ }\right)$

$\Rightarrow \frac{1}{\sqrt{3}}$

option A is correct.