If $a\cos \theta -b\sin \theta =c$, then $a\sin \theta +b\cos \theta =$

$a\cos \theta -b\sin \theta =c$

$a\sin \theta +b\cos \theta =?$

$a\cos \theta -b\sin \theta =c$

$a\sin \theta +b\cos \theta =k$

$a\cos \theta -b\sin \theta =c$

${(a\cos \theta -b\sin \theta )}^2=c^2$

$a\sin \theta +b\cos \theta =k$

${(a\sin \theta +b\cos \theta )}^2=k^2$

$c^2+k^2=a^2{\cos }^2\theta +b^2{\sin }^2\theta$

$+a^2{\sin }^2\theta +b^2{\cos }^2\theta$

$c^2+k^2=a^2+b^2$

$k^2=a^2+b^2-c^2$

$k=\pm \sqrt{a^2+b^2-c^2}$