Question

The value of $(1+cos\frac{\pi }{8})(1+cos\frac{3\pi }{8})(1+cos\frac{5\pi }{8})(1+cos\frac{7\pi }{8})$ is equal to

• A. $\frac{1}{4}$
• B. $\frac{1}{6}$
• C. $\frac{1}{8}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $\frac{1}{8}$

$(1+cos\frac{\pi }{8})(1+\cos \frac{3\pi }{8})(1-\cos \frac{3\pi }{8})(1-\cos \frac{\pi }{8})=(1-{\cos }^2(\pi /8\left)\right)(1-{\cos }^2(3\pi /8\left)\right)={\sin }^2\left(3\pi /8\right){\sin }^2\left(\pi /8\right)=1/4(1-\cos \left(\pi /4\right))(1-\cos \left(3\pi /4\right))=1/8$