A) \[1\]
B) \[\frac{3}{2}\]
C) 2
D) \[\frac{5}{2}\]
Correct Answer: C
Solution :
\[{{\sin }^{2}}\frac{\pi }{8}+{{\sin }^{2}}\frac{3\pi }{8}+{{\sin }^{2}}\frac{5\pi }{8}+{{\sin }^{2}}\frac{7\pi }{8}\] \[{{\sin }^{2}}\frac{\pi }{8}+{{\sin }^{2}}\frac{3\pi }{8}+{{\sin }^{2}}\left( \pi -\frac{3\pi }{8} \right)+{{\sin }^{2}}\left( \pi -\frac{\pi }{8} \right)\]\[{{\sin }^{2}}\frac{\pi }{8}+{{\sin }^{2}}\frac{3\pi }{8}+{{\sin }^{2}}\frac{3\pi }{8}+{{\sin }^{2}}\frac{\pi }{8}\] \[=2\left[ {{\sin }^{2}}\,\frac{\pi }{8}+{{\sin }^{2}}\frac{3\pi }{8} \right]\] \[=2\left[ {{\sin }^{2}}\frac{\pi }{8}+{{\sin }^{2}}\left( \frac{\pi }{2}-\frac{\pi }{8} \right) \right]\] \[=2\left[ {{\sin }^{2}}\frac{\pi }{8}+{{\cos }^{2}}\frac{\pi }{8} \right]\] \[=2.1=2\]
You need to login to perform this action.
You will be redirected in
3 sec
