SOLUTION: prove the following is an identity sin(theta+60degrees) + cos(theta+30degrees)= sqr3costheta

Question 519102: prove the following is an identity
sin(theta+60degrees) + cos(theta+30degrees)= sqr3costheta
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
prove the following is an identity
sin(theta+60degrees) + cos(theta+30degrees)= sqr3costheta
**
x=theta
sin(x+60)+cos(x+30)=√3cosx
starting with left side, using addition formulas for sin and cos
sin(x+60)=sinxcos60+cosxsin60
=sinx/2+√3cosx/2
..
cos(x+30)=cosxcos30-sinxsin30
=cosx√3/2-sinx/2
..
sin(x+60)+cos(x+30)
=sinx/2+√3cosx/2+cosx√3/2-sinx/2
=√3cosx
verified: left side=right side
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