SOLUTION: If the cos x is -(1/2) and the x is in the 2nd quadrant, find the cos 2x. (no calculator) I have been working on this problem for 30 mins. I think I am missing one thing for it

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Question 816468: If the cos x is -(1/2) and the x is in the 2nd quadrant, find the cos 2x. (no calculator)
I have been working on this problem for 30 mins. I think I am missing one thing for it to make sense. I think that sin x= 2/sq.rt. 5...
Show that this is a trig identity.
csc^2 = cot^2x+1
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
If the cos x is -(1/2) and the x is in the 2nd quadrant, find the cos 2x.
cos(2x)=cos^2(x)-sin^2(x)
..
cos(x)=(-1/2)
cos^2(x)=1/4
..
sin(x)=√3/2
sin^2(x)=3/4
..
cos(2x)=(1/4)-(12/16)=(4/16)-(12/16)=-8/16=-1/2
...
Show that this is a trig identity.
csc^2x = cot^2x+1
start with right side:
cot^2x+1=cos^2/sin^2x+1
(sin^2(x)+cos^2(x))/sin^2(x)
1/sin^2(x)=csc^2(x)
verified:
right side=left side