A) \[2/3\]
B) \[\frac{2}{3+\sqrt{3}}\]
C) \[3/2\]
D) \[\frac{3+\sqrt{3}}{2}\]
Correct Answer: C
Solution :
\[={{\cos }^{2}}\frac{\pi }{4}+{{\cos }^{2}}\frac{\pi }{12}+{{\cos }^{2}}\frac{5\pi }{12}\] \[=\frac{1}{2}+{{\cos }^{2}}\frac{\pi }{12}+-{{\sin }^{2}}\frac{5\pi }{12}\] \[=\frac{3}{2}+{{\cos }^{2}}\frac{\pi }{12}-{{\sin }^{2}}\frac{5\pi }{12}\] \[=\frac{3}{2}+\cos \left( \frac{\pi }{12}+\frac{5\pi }{12} \right)\cos \left( \frac{\pi }{12}-\frac{5\pi }{12} \right)\] \[=\frac{3}{2}+\cos \left( \frac{6\pi }{12} \right)\cos \left( \frac{-4\pi }{12} \right)\Rightarrow \frac{3}{2}+0=\frac{3}{2}\]
You need to login to perform this action.
You will be redirected in
3 sec
