Question #616b5

2 Answers
P dilip_k
Feb 11, 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#

Sean
Feb 11, 2018

#sintheta-costheta=(2-sqrt2)sintheta#

Explanation:

.

#costheta+sintheta=sqrt2sintheta#

#costheta=sqrt2sintheta-sintheta#

#costheta=(sqrt2-1)sintheta#

#sintheta-costheta=sintheta-(sqrt2-1)sintheta#

#sintheta-costheta=sintheta(1-sqrt2+1)#

#sintheta-costheta=(2-sqrt2)sintheta#

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