If #Cos theta +sin theta = sqrt2 sin theta# then #sin theta - cos theta#?

1 Answer
P dilip_k
Feb 8, 2018

Given #Cos theta +sin theta = sqrt2 sin theta#

Now

#(sintheta+costheta)^2+(sin theta - cos theta)^2=2(sin^2theta+cos^2theta)#

#=>(sqrt2sintheta)^2+(sin theta - cos theta)^2=2#

#=>(sin theta - cos theta)^2=2-2sin^2theta#

#=>(sin theta - cos theta)^2=2(1-sin^2theta)=2cos^2theta#

#=>sin theta - cos theta=pmsqrt2costheta#

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