Question

Value of $\frac{{\cos }^2{15}^o+{\sin }^2{15}^o}{{\cos }^2{15}^o-{\sin }^2{15}^o}$ will be

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

Answer 1

The correct option is D $\frac{2}{\sqrt{3}}$

$co{s}^{2}A+si{n}^{2}A=1$

Hence numerator = 1

${\cos }^2\left(\frac{A}{2}\right)=\frac{1+\cos A}{2}$

$⟹{\cos }^{2}15=\frac{1+\cos 30}{2}=\frac{2+\sqrt{3}}{4}$

${\sin }^{2}15=\frac{1-\cos 30}{2}=\frac{2-\sqrt{3}}{4}$

Dinominator = $\frac{\sqrt{3}}{2}$

Hence the given equation: $\frac{2}{\sqrt{3}}$