$A=\dfrac{1}{\sin 10°} - 4\sin 70°$
$= \dfrac{1- 4\sin 70°. \sin 10°}{\sin 10°}$
$= \dfrac{1-4.\dfrac{-1}{2}.\Big[ \cos 80° - \cos 60° \Big]}{\sin 10°}$
$= \dfrac{1-2.(\sin 30° - \sin 10°)}{\sin 10°}$
$= \dfrac{2 \sin 10°}{\sin 10°}=2$
$B= \cos 14° + \cos 134° + \cos 106°$
$= 2. \cos 74°. \cos (-60°) + \cos 106°$
$= 2 \cos 74°. \dfrac{1}{2} + \cos 106°$
$= \cos 74° + \cos 106°$
$=2.\cos 90°. \cos (-16°)$
$= 2.0.\cos (-16°)$
$=0$
$C= \sin^4\dfrac{\pi}{16}+\sin^4\dfrac{3\pi}{16} + \sin^4 \dfrac{5\pi}{16}+\sin^4 \dfrac{7\pi}{16}$
$=\Big(\dfrac{1-\cos \dfrac{\pi}{8}}{2}\Big)^2+\Big(\dfrac{1-\cos \dfrac{3\pi}{8}}{2}\Big)^24\Big(\dfrac{1-\cos \dfrac{5\pi}{8}}{2}\Big)^2+\Big(\dfrac{1-\cos \dfrac{7\pi}{8}}{2}\Big)^2$
$= \dfrac{1}{4}.\Big(1-2\cos \dfrac{\pi}{8}+ \cos^2\dfrac{\pi}{8}+1-2\cos \dfrac{3\pi}{8} + \cos^2\dfrac{3\pi}{8}+1-2\cos \dfrac{5\pi}{8} + \cos^2 \dfrac{5\pi}{8}+1-2\cos \dfrac{7\pi}{8}+\cos^2 \dfrac{7\pi}{8} \Big)$
`=3/2`
