A) Zero
B) Two
C) One
D) Infinite
Correct Answer: B
Solution :
\[3\cos \theta +4\sin \theta =5\,\left[ \frac{3}{5}\cos \theta +\frac{4}{5}\sin \theta \right]=5\cos (\theta -\alpha )\] where \[\cos \alpha =\frac{3}{5}\], \[\sin \alpha =\frac{4}{5}\] Now \[3\cos \theta +4\sin \theta =k\] \ \[5\cos (\theta -\alpha )=k\Rightarrow \cos (\theta -\alpha )=\pm 1\] \[\Rightarrow \] \[\theta -\alpha ={{0}^{o}},\,{{180}^{o}}\Rightarrow \theta =\alpha ,\,\text{ }{{180}^{o}}+\alpha \].
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