Let $a$ and $b$ be non-negative real numbers. If $\sin x+a \cos$ $\mathrm{x}=\mathrm{b}$, then $|\mathrm{a}…
Let $a$ and $b$ be non-negative real numbers. If $\sin x+a \cos$ $\mathrm{x}=\mathrm{b}$, then $|\mathrm{a} \sin \mathrm{x}-\cos \mathrm{x}|=$
$\sqrt{a^2-b^2+1}$
$\sqrt{b^2-a^2+1}$
$\sqrt{1+a^2+b^2}$
$\sqrt{a^2+b^2-1}$
Solution
Given $\sin \mathrm{x}+\mathrm{a} \cos \mathrm{x}=\mathrm{b}...(i)$
Let $a \sin \mathrm{x}-\cos \mathrm{x}= \pm \alpha...(ii)$
on squanity and adding (i) and (ii)
we got $\mathrm{a}^2+1=\mathrm{b}^2+\alpha^2$
$
\Rightarrow \alpha \sqrt{\mathrm{a}^2-\mathrm{b}^2+1}
$