Question

$\frac{{\cot }^{2}15^{\circ }-1}{{\cot }^{2}15^{\circ }+1}=$

• A. $\frac{1}{2}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{3\sqrt{3}}{2}$
• D. $\frac{\sqrt{3}}{4}$

Answer 1

Answer: (B)

$\frac{{\cot }^{2}15-1}{{\cot }^{2}15+1}=\frac{{\cos }^{2}15-{\sin }^{2}15}{{\cos }^{2}15+{\sin }^{2}15}={\cos }^{2}15-{\sin }^{2}15$
$=\cos 15\cos 15-\sin 15\sin 15$
$=\cos (15+15)=\cos 30^{\circ }=\frac{\sqrt{3}}{2}$