Trigonometric Identities Question 73
Question: $ {{\sin }^{2}}\frac{\pi }{8}+{{\sin }^{2}}\frac{3\pi }{8}+{{\sin }^{2}}\frac{5\pi }{8}+{{\sin }^{2}}\frac{7\pi }{8}= $
Options:
A) 1
B) -1
C) 0
D) 2
Show Answer
Answer:
Correct Answer: D
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}}\frac{3\pi }{8}+{{\sin }^{2}}\frac{\pi }{8} $ $ =2( {{\sin }^{2}}\frac{\pi }{8}+{{\sin }^{2}}\frac{3\pi }{8} )=2\times 1=2 $ .
BETA
