A) [?1, 3]
B) [1, 1]
C) [0, 1]
D) [0, ?1]
Correct Answer: A
Solution :
\[-\sqrt{1+{{(-\sqrt{3})}^{2}}}\le (\sin x-\sqrt{3}\cos x)\le \sqrt{1+{{(-\sqrt{3})}^{2}}}\] \[-2\le (\sin x-\sqrt{3}\cos x)\le 2\] \[-2+1\le (\sin x-\sqrt{3}\cos x+1)\le 2+1\] \[-1\le (\sin x-\sqrt{3}\cos x+1)\le 3\] i.e., range \[=[-1,\,\,3]\] \ For f to be onto \[S=[-1,\,\,3]\].
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