A) \[\frac{1}{2}\]
B) \[\frac{1}{8}\]
C) \[\cos \frac{\pi }{8}\]
D) \[\frac{1+\sqrt{2}}{2\sqrt{2}}\]
Correct Answer: B
Solution :
\[\left( 1+\cos \frac{\pi }{8} \right)\left( 1+\cos \frac{3\pi }{8} \right)\left( 1-\cos \frac{3\pi }{8} \right)\] \[\left( 1-\cos \frac{\pi }{8} \right)\] \[=\left( 1-{{\cos }^{2}}\frac{\pi }{8} \right)\left( 1-{{\cos }^{2}}\frac{3\pi }{8} \right)\] \[={{\left( \sin \frac{\pi }{8}\sin \frac{3\pi }{8} \right)}^{2}}\] \[=\frac{1}{4}{{\left( 2\sin \frac{3\pi }{8}\sin \frac{\pi }{8} \right)}^{2}}\] \[=\frac{1}{4}{{\left( \cos \frac{\pi }{4}-\cos \frac{\pi }{2} \right)}^{2}}=\frac{1}{8}\]
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