If $0 \leq x \leq \pi$ and $81^{\sin ^2 x}+81^{\cos ^2 x}=30$ Then $x$ takes the value

$$ \cos ^4 \frac{\pi}{8}+\cos ^4 \frac{3 \pi}{8}+\cos ^4 \frac{5 \pi}{8}+\cos ^4 \frac{7 \pi}{8}= $$

If $\sec x+\tan x=2,0 < x < \frac{\pi}{2}$ then $\sin \frac{x}{4}=$

The maximum value of the function $a \sin x+b \cos x$ is