A) \[[-\sqrt{2},\,\,\sqrt{2}]\]
B) \[[0,\,\,\sqrt{2}]\]
C) \[[1,\,\,\sqrt{2}]\]
D) \[[-1,\,\,\sqrt{2}]\]
Correct Answer: D
Solution :
Use \[-1\le \,\sin \,x\,\le 1\] and \[0\le \,|\,\cos \,x|\,\le 1\] and \[-\sqrt{{{a}^{2}}+{{b}^{2}}}\le a\] \[-\sqrt{{{a}^{2}}+{{b}^{2}}}\le a\,\cos \,x+b\,\sin \,x\,\le \,\sqrt{{{a}^{2}}+{{b}^{2}}}\]
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