The one I'm thinking of right now is to convert the cos^(2)x into 1/2 [cos2x + 1] and then convert 7sinxcosx into 7/2 sin2x (double angle). Then expand and collect al the trigonometric functions to one side and constants on the other. You'll get something like cos2x + 7sin2x = 5
Then transform the LHS into one trigonometric function eg. Rcos (2x-a) and use fundamental formula from there