SOLUTION: If cos(x+pi/6)+sin(x−pi/3)=A, then the number A=

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Question 681741: If cos(x+pi/6)+sin(x−pi/3)=A, then
the number A=
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If cos(x+pi/6)+sin(x−pi/3)=A, then
the number A=
**
Use addition formulas:
cos(x+π/6)=cosx*cosπ/6-sinx*sin(π/6)=cosx*√3/2-sinx*(1/2)
sin(x−π/3)=sinx*cos(π/3)-cosx*sin(π/3)=sinx*(1/2)-cosx*√3/2
A= cos(x+pi/6)+sin(x−pi/3)
A=cosx*√3/2-sinx*(1/2)+sinx*(1/2)-cosx*√3/2=0
A=0