NIMCET 2014 Question Paper with solutions

We have,
sinx + acosx = b
On squaring both sides, we get
$\mathit{s}\mathit{i}{\mathit{n}}^2\mathit{x}$ + ${\mathit{a}}^2\mathit{c}\mathit{o}{\mathit{s}}^2\mathit{x}$ + 2asinx cosx = ${\mathit{b}}^2$
⇒ 1 - $\mathit{c}\mathit{o}\mathit{s}2\mathit{x}$ + ${\mathit{a}}^2$ - ${\mathit{a}}^2\mathit{s}\mathit{i}{\mathit{n}}^2\mathit{x}$ + 2asinx cosx = ${\mathit{b}}^2$
⇒ ${\mathit{a}}^2\mathit{s}\mathit{i}{\mathit{n}}^2\mathit{x}$ + $\mathit{c}\mathit{o}{\mathit{s}}^2\mathit{x}$ - 2asinxcosx = 1 + ${\mathit{a}}^2-{\mathit{b}}^2$
⇒ ${\left(\mathit{a}\mathit{s}\mathit{i}\mathit{n}\mathit{x}-\mathit{c}\mathit{o}\mathit{s}\mathit{x}\right)}^2$ = 1 + ${\mathit{a}}^2-{\mathit{b}}^2$
⇒ |asinx - cosx| = $\sqrt{1+{\mathit{a}}^2-{\mathit{b}}^2}$