Question

The value of ${\cos }^4\left(\frac{\pi }{4}\right)-{\cos }^4\left(\frac{\pi }{6}\right)+{\sin }^4\left(\frac{\pi }{6}\right)+{\sin }^4\left(\frac{\pi }{3}\right)$ is

• A. $\frac{1}{16}$
• B. $\frac{1}{8}$
• C. $\frac{5}{16}$
• D. $\frac{3}{16}$

Answer 1

The correct option is C $\frac{5}{16}$

${\cos }^4\pi /4-{\cos }^4\pi /6+{\sin }^4\pi /6+{\sin }^4\pi /3={\cos }^4\pi /4+{\sin }^4\pi /6\Rightarrow \frac{1}{4}+\frac{1}{16}=\frac{5}{16}$