Question #88774

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Answer 1 · 2016-12-11T08:31:35

We know

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

$=>(sqrt2costheta)^2+(costheta-sintheta)^2=2xx1$

$=>(costheta-sintheta)^2=2-2cos^2theta$

$=>(costheta-sintheta)^2=2(1-cos^2theta)$

$=>(costheta-sintheta)^2=2sin^2theta$

$=>costheta-sintheta=sqrt2sintheta$