A) \[x=\frac{n\pi }{2},\]\[n\in Z\]
B) \[x=n\pi ,\]\[n\in Z\]
C) \[x=(2n+1)\pi ,\]\[n\in Z\]
D) none of these
Correct Answer: B
Solution :
We have, \[\tan 3x=\tan 5x\] \[\Rightarrow \] \[5x=n\pi +3x,\] \[n\in Z\]\[\Rightarrow \]\[x=\frac{n\pi }{2},\] \[n\in Z\] If n is odd, then \[x=\frac{n\pi }{2}\] gives extraneous solutions. Thus, the solution of the given equation will be given by \[x=\frac{n\pi }{2},\] where n is even, say \[n=2m,\]\[m\in Z.\] Hence the required solution is \[x=m\pi ,\]\[m\in Z.\]
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