Question

Find the value of the expression $co{s}^4\frac{\pi }{8}+co{s}^4\frac{3\pi }{8}+co{s}^4\frac{5\pi }{8}+co{s}^4\frac{7\pi }{8}$

Or

Find the value of $sin\frac{x}{2},cos\frac{x}{2}$ and $tan\frac{x}{2}$, if $sinx=\frac{1}{4}$, where x lies in ssecond quadrant.

Answer 1

$\frac{3}{2}$

Or

$sin\frac{x}{2}=\sqrt{\frac{4+\sqrt{15}}{8}},tan\frac{x}{2}=4+\sqrt{15},cos\frac{x}{2}=\sqrt{\frac{4-\sqrt{15}}{8}}$