Let a and b be non-negative real numbers. If | vedclass

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(A) Given $\sin x + a \cos x = b$ ... $(i)$ Let $y = |a \sin x - \cos x|$. Squaring both equations: $(\sin x + a \cos x)^2 = b^2$ $\sin^2 x + a^2 \cos

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$\sqrt{a^2 - b^2 + 1}$

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(A) Given $\sin x + a \cos x = b$ ... $(i)$ Let $y = |a \sin x - \cos x|$. Squaring both equations: $(\sin x + a \cos x)^2 = b^2$ $\sin^2 x + a^2 \cos^2 x + 2a \sin x \cos x = b^2$ ... $(ii)$ $(a \sin x - \cos x)^2 = y^2$ $a^2 \sin^2 x + \cos^2 x - 2a \sin x \cos x = y^2$ ... $(iii)$ Adding $(ii)$ and $(iii)$: $(\sin^2 x + a^2 \cos^2 x) + (a^2 \sin^2 x + \cos^2 x) = b^2 + y^2$ $\sin^2 x (1 + a^2) + \cos^2 x (a^2 + 1) = b^2 + y^2$ $(a^2 + 1)(\sin^2 x + \cos^2 x) = b^2 + y^2$ $a^2 + 1 = b^2 + y^2$ $y^2 = a^2 - b^2 + 1$ $y = \sqrt{a^2 - b^2 + 1}$

Let $a$ and $b$ be non-negative real numbers. If $\sin x + a \cos x = b$,then $|a \sin x - \cos x| = $

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