how can i solve for x given this?? pls. show detailed solution..just can't figure it out.thanks in advance!
6cosx+3cos35cosx-3sin35sinX=7cosx
3cos35cosx-3sin35sinX = 3cos(x+35)
So, now you have
3cos(x+35)-cosx = 0
Hmmm. not much help. So, back to basics.
6cosx+3cos35cosx-3sin35sinX=7cosx
3sin35 sinx = (1-3cos35) cosx
Let c = (1-3cos35)/(3sin35) = -0.847 and you have
sinx = c cosx
sin^2x = c^2 cos^2c
1-cos^2x = c^2 cos^2x
(1+c^2)cosx = 1
cosx = 1/(1+c^2) = 0.5823
Now you can find x; check for solutions in other quadrants.