Question 1048799
<pre><b>{{{7cos(x) + 8cos(x-"60°")}}}{{{""=""}}}

{{{7cos(x) + 8(cos(x)^""cos("60°") + sin(x)sin("60°")))}}}{{{""=""}}}

{{{7cos(x) + 8(cos(x)^""(1/2) + sin(x)(sqrt(3)/2)))}}}{{{""=""}}}

{{{7cos(x) + 4cos(x) + 4sqrt(3)sin(x)}}}{{{""=""}}}

{{{11cos(x) + 4sqrt(3)sin(x)}}}

Draw a right triangle with opposite side 11 and adjacent
side {{{4sqrt(3)}}}, and angle y

{{{drawing(100,200,-.5,2,-.5,1.5,line(-3,0,3,0),line(0,-3,0,3), line(0,0,1.5,1),line(1.5,0,1.5,1),locate(.4,.2,y), locate(1.53,.62,11),locate(.77,-.05,4sqrt(3)),locate(.6,.7,r) )}}} 

Then {{{r=sqrt(11^2+(4sqrt(3))^2) = sqrt(121+16*3) = sqrt(121+48)=sqrt(169)=13}}}

{{{drawing(100,200,-.5,2,-.5,1.5,line(-3,0,3,0),line(0,-3,0,3), line(0,0,1.5,1),line(1.5,0,1.5,1),locate(.4,.2,y), locate(1.53,.62,11),locate(.77,-.05,4sqrt(3)),locate(.3,.6,13) )}}} 

And {{{ y=arctan(11/(4sqrt(3))) = "57.79577249°"}}}

{{{11/13=sin(y)}}}, {{{4sqrt(3)/13=cos(y)}}}

{{{11=13*sin(y)}}}, {{{4sqrt(3)=13*cos(y)}}}

Substitute for 11 and {{{4sqrt(3)}}} in

{{{11cos(x) + 4sqrt(3)sin(x)}}}{{{""=""}}}

{{{13*sin(y)cos(x) + 13*cos(y)sin(x)}}}{{{""=""}}}

{{{13(sin(y)cos(x)^"" + cos(y)sin(x))}}}{{{""=""}}}

{{{13(sin(y+x)^"")}}}{{{""=""}}}

{{{13sin(x+y))}}}{{{""=""}}}

{{{13sin(x+"57.79577249°"))}}}
 
Edwin</pre></b>