How do you prove that #2cos(theta+pi/3) = costheta-sqrt3sintheta#?

1 Answer
Lucy
May 26, 2018

Below

Explanation:

#2cos(theta+pi/3)=costheta-sqrt3sintheta#

LHS
#2cos(theta+pi/3)#

Recall: #cos(a-b)=cosacosb-sinasinb#

= #2(costhetacos(pi/3)-sinthetasin(pi/3))#

= #2(costhetatimes1/2-sinthetatimessqrt3/2)#

= #2times1/2timescostheta-1/2timessqrt3/2timessintheta#

= #costheta-sqrt3sintheta#

= RHS

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