Statement-1: The period of sinx , cos x is `2pi` and period of f(x)+g(x) is the LCM of the periods of f(x) and g(x)

Options

A. Statement-1 is True, Statement-2 is True, statement-2 is a correct explanation for the statement-1 .
B. Statement-1 is True, Statement-2 is True, statement-2 is not a correct explanation for the statement-1 .
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False , Statement-2 is True.

Answer

A

Explanation

Clearly, Statement-2 is true .
Now,
` sin""(pi)/(4)[x]=sin(2pi+(pi)/(4)[x])=sin""(pi)/(4)(8+[x])=sin""(pi)/(4)[x+8]`
`implies sin""(pi)/(4)[x]` is periodic with period 3.
`cot""(pi)/(3)[x]=cot(pi+(pi)/(3)[x])=cot""(pi)/(3)[3+[x])=cot""(pi)/(3)[x+3]`
`implies cot""(pi)/(3)[x]` is periodic with period 3.
and , ` cos""(pix)/(2)` is periodic with period `(2pi)/(pi//2)=4`
Using statement-2, period of f(x) is LCM of (8,3,4)=24