If #sin(theta)+cos(theta)=sqrt(3)cos(theta)#, then what is the value of #2cos(theta)-sin(theta)# from the following option?

Question

#a)sqrt{3}sin(theta)#
#b)-sqrt{3}sin(theta)#

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Answer 1 · 2018-01-12T14:26:02

#sintheta+ costheta=sqrt3costheta#

#=>sintheta=sqrt3costheta-costheta#

#=>sintheta=(sqrt3-1)costheta#

#=>sintheta/costheta=(sqrt3-1)#

#=>sintheta/costheta=((sqrt3-1)(sqrt3+1))/(sqrt3+1)#

#=>sintheta/costheta=((sqrt3)^2-1^2)/(sqrt3+1)#

#=>sintheta/costheta=2/(sqrt3+1)#

#=>2costheta=sqrt3sintheta+ sintheta#

#=>2costheta-sintheta=sqrt3sintheta#

So option (a) #sqrt3sintheta# accepted