| Statement 1: Period of \[f(x)=\sin \,\frac{\pi x}{(n-1)!}\cos \frac{\pi x}{n!}\] is \[2(n!)\] |
| Statement 2: Period of \[|\cos x|+|\sin x|+3\] is \[\pi \] |
A) Both statements are true, and Statement-2 explains Statement-1.
B) Both statements are true, but Statement-2 does not explain Statement-1.
C) Statement-1 is True, Statement-2 is False.
D) Statement-1 is False, Statement-2 is true.
Correct Answer: C
Solution :
Period of \[\sin \frac{\pi x}{(n-1)!}=2(n-1)!\] Period of \[\cos \frac{\pi x}{n!}=2(n!)\] \[\Rightarrow \] Period of \[f(x)=LCM\] of \[2((n-1)!)\] and \[2(n!)=2(n!)\] And period of \[f(x)=|\cos x|+|\sin x|+3\] is \[\frac{\pi }{2}\].
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