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

1 answer

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.
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