if cos theta +sin theta=1,then prove that cos theta-sin theta=(+) or (-) 1 ?

1 Answer
Aug 14, 2017

Using the formula

(a+b)^2+(a-b)^2=2(a^2+b^2)

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

=>1^2+(costheta-sintheta)^2=2xx1

=>(costheta-sintheta)^2=2-1=1

=>costheta-sintheta=pm1