Question

The value of $\frac{1-ta{n}^{2}15^{\circ }}{1+ta{n}^{2}15^{\circ }}$ is

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

Answer 1

Answer: (C)

$\frac{1-ta{n}^{2}15^{\circ }}{1+ta{n}^{2}15^{\circ }}=\frac{co{s}^{2}15^{\circ }-si{n}^{2}15^{\circ }}{co{s}^{2}15^{\circ }+si{n}^{2}15^{\circ }}$
$=\frac{cos\left(2\times 15^{\circ }\right)}{1}$
$=cos30^{\circ }=\frac{\sqrt{3}}{2}$