Question #1ba12

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Answer 1 · 2017-10-08T17:07:20

See below.

Using identities:

#color(red)(sin(A+B) = sinAcosB+cosAsinB)#

#color(red)(cos(A-B)=cosAcosB-sinAsinB)#

#4[cos(x)cos(pi/6)+sin(x)sin(pi/6)]= 3[sin(x)cos(pi/3)+cos(x)sin(pi/3)]#

#4[cos(x)cos(pi/6)]-3[cos(x)sin(pi/3)]=3[sin(x)cos(pi/3)]-4[sin(x)sin(pi/6)]#

Factor:

#cos(x)[4cos(pi/6)-3sin(pi/3)]=sin(x)[3cos(pi/3)-4sin(pi/6)]#

#cos(x)[sqrt(3)/2]=sin(x)[-1/2]#

#(sin(x))/(cos(x))=(sqrt(3)/2)/(-1/2)#

#(sin(x))/(cos(x))= -sqrt(3)=> tan(x)= -sqrt(3)#

#arctan(tan(x))= arctan(-sqrt(3))= -pi/3#