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Answer 1 · 2017-04-26T17:05:36

#50.1^o, 154.3^o, 205.7^o, 309.0^o#

Start by completing the square as this expression cannot be factorised.

#3cos^2x+cosx-1=0#

#cos^2x+1/3cosx-1/3=0#

#(cosx-1/6)^2-1/36-1/3=0#

#(cosx-1/6)^2 = 13/36#

#cosx-1/6 = +-sqrt(13/36)#

#cosx=1/6 +-sqrt(13)/6#

#cosx=1/6(1 +-sqrt(13))#

Now we look at a graph to see where the solutions will lie.

Geogebra

The graph shows solutions in radians. Solutions in degrees are as follows

#50.1^o, 154.3^o, 205.7^o, 309.0^o#