A) \[\theta \in R\]
B) \[\theta =\frac{n\pi }{2},n\in Z\]
C) \[\theta \in R-n\pi ,\,\,n\in Z\]
D) \[\theta \in R-\frac{n\pi }{2},\,n\in Z\]
Correct Answer: D
Solution :
[d] \[\frac{3\sin \theta -\sin 3\theta }{\sin \theta }+\frac{\cos 3\theta }{\cos \theta }=1\] \[\Rightarrow \,\,\,\frac{4{{\sin }^{3}}\theta }{\sin \theta }+\frac{(4{{\cos }^{3}}\theta -3\cos \theta )}{\cos \theta }=1\] \[\Rightarrow \,\,4{{\sin }^{2}}\theta +4{{\cos }^{2}}\theta -3=1\Rightarrow 1=1\] (identity) Which is always true except\[\theta =\frac{n\pi }{2}\].
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