Question

Can anyone help me find out what to do next?
http://i.imgur.com/X7sm5IH.jpg
That's all I got so far.

Answer 1

You can't find a solution for cotx = 3 without a calculator. Leave it as:
x = arccot3

Answer 2

\[\cot x=3,\csc ^{2}x-\cot ^{2}x=1,\csc ^{2}x=1+\cot ^{2}x=1+9=10,\sin ^{2}x=\frac{ 1 }{ 10 }\]
\[\cos 2x=1-2\sin ^{2}x=1-\frac{ 1 }{5 }=\frac{ 4 }{5 },x=\frac{ 1 }{2 }\cos^{-1} \frac{ 4 }{5 }\]

Answer 3

you can also write as zarax has written