Q76 / 180 · COMEDK 2018 · Mathematics
$\cos ^{2} \frac{\pi}{12}+\cos ^{2} \frac{\pi}{4}+\cos ^{2} \frac{5 \pi}{12}=$
- Correct answerA$\frac{3}{2}$
- B$\frac{3-\sqrt{3}}{2}$
- C$\frac{2}{3}$
- D$\frac{2}{3+\sqrt{3}}$
Solution
$$
\begin{aligned}
& \cos ^{2} \frac{\pi}{12}+\cos ^{2} \frac{\pi}{4}+\cos ^{2} \frac{5 \pi}{12} \\
=& \cos ^{2} \frac{\pi}{12}+\cos ^{2} \frac{\pi}{4}+\cos ^{2}\left(\frac{\pi}{2}-\frac{\pi}{12}\right) \\
=& \cos ^{2} \frac{\pi}{12}+\cos ^{2} \frac{\pi}{4}+\sin ^{2} \frac{\pi}{12} \\
=& 1+\cos ^{2} \frac{\pi}{4}=1+\left(\frac{1}{\sqrt{2}}\right)^{2}=1+\frac{1}{2}=\frac{3}{2}
\end{aligned}
$$
Hence, the correct answer is option: 'A'.