Answer
(a) $sin~2u=\frac{\sqrt 3}{2}$
(b) $cos~2u=-\frac{1}{2}$
(c) $tan~2u=-\sqrt 3$
Work Step by Step
$cos~u=\frac{1}{sec~u}=-\frac{1}{2}$
$sin^2u+cos^2u=1$
$sin^2u+(-\frac{1}{2})^2=1$
$sin^2u=1-\frac{1}{4}=\frac{3}{4}$
$sin~u=-\frac{\sqrt 3}{2}~~~~$ ($\pi\lt u\lt\frac{3\pi}{2}$)
$tan~u=\frac{sin~u}{cos~u}=\frac{-\frac{\sqrt 3}{2}}{-\frac{1}{2}}=\sqrt 3$
(a) $sin~2u=2~sin~u~cos~u=2(-\frac{\sqrt 3}{2})(-\frac{1}{2})=\frac{\sqrt 3}{2}$
(b) $cos~2u=cos^2u-sin^2u=\frac{1}{4}-\frac{3}{4}=-\frac{1}{2}$
(c) $tan~2u=\frac{2~tan~u}{1-tan^2u}=\frac{2\sqrt 3}{1-(\sqrt 3)^2}=\frac{2\sqrt 3}{-2}=-\sqrt 3$
