SOLUTION: Simplify: a)((cos120)/cos330)) - ((sin90)/cos315)) b) (sin^2 210)/ (3cos^2 120+cos150)

Algebra ->  Trigonometry-basics -> SOLUTION: Simplify: a)((cos120)/cos330)) - ((sin90)/cos315)) b) (sin^2 210)/ (3cos^2 120+cos150)      Log On


   

Question 260476: Simplify:
a)((cos120)/cos330)) - ((sin90)/cos315))
b) (sin^2 210)/ (3cos^2 120+cos150)
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
a)%28%28cos120%29%2Fcos330%29+-+%28%28sin90%29%2Fcos315%29+
cos 120 = -1/2
cos 330 = sqrt(3)/2
sin 90 = 1
cos 315 = sqrt(2)/2
so, we get
%28-1%2F2%29%2F%28sqrt%283%29%2F2%29+-+1%2F%28sqrt%282%29%2F2%29
which is
-sqrt%283%29+-+2%2Fsqrt%282%29
and finally
-sqrt%283%29+-+sqrt%282%29
--
b) (sin^2 210)/ (3cos^2 120+cos150)
sin 210 = -1/2
sin^2(210) = 1/4
cos 120 = -1/2
cos^2(120) = 1/2
3cos^2(120) = 3/2
cos150 = -sqrt(3)/2
so, we get
%281%2F4%29%2F%283%2F2-sqrt%283%29%2F2%29%29
which becomes
1%2F%282%2A%283-sqrt%283%29%29%29
rationalizing, we get
%283%2B+sqrt%283%29%29%2F12