Question

UNKNOWN:
http://prntscr.com/9awnmp (Where did I do this wrong?)

OK:
http://prntscr.com/9avznx [ SOLVED ]
http://prntscr.com/9aw36d [ SOLVED ]
http://prntscr.com/9aw479 [ SOLVED ]
http://prntscr.com/9awjbz [ SOLVED ]

Answer 1

\[\cos2x=\frac{ \sqrt{3} }{ 2 }\]

Here you might want to perform a change of variable, since the double angle can come up with some problems so:
\[\cos(2x) = \frac{ \sqrt{3} }{ 2 }\]
\[u=2x\]
\[\iff Cos(u)=\frac{ \sqrt{3} }{ 2 }\]

Now with the easy part away, we must take into consideration the solutions for the angle "u" to then translate it into the solutions for the "x" variable.
That is the very essence when performing a change of variable, solve for the new variable in order to solve much more comfortably for the original one.
So, for "u" we will have two solutions U1 and U2:
\[u_1=\frac{ \pi }{ 6 }\]
\[u_2=\frac{ 2 \pi }{ 3 }\]
This will translate into two solutions for the "x" variable:
\[2x_1=\frac{ \pi }{ 6 }\]
\[2x_2=\frac{ 2 \pi }{ 3 }\]
I'll let you take if from here, remember to be careful when choosing your solutions.

Answer 2

meow meow kitty witty :)
You didn't do anything wrong,
you simply forgot to simplify all the way.

Answer 3

Maybe I'm misunderstanding the way the webpage is setup...
is the green box the correct answer to the first box?
Or is that a separate question?

Answer 4

@kittiwitti1

Look at @isuru 's work at

http://openstudy.com/study#/updates/5254841fe4b037f058868e5a