JEE Advance - Mathematics (2007 - No. 8)
Let $$F(x)$$ be an indefinite integral of $$si{n^2}x.$$
STATEMENT-1: The function $$F(x)$$ satisfies $$F\left( {x + \pi } \right) = F\left( x \right)$$
for all real $$x$$. because
STATEMENT-2: $${\sin ^2}\left( {x + \pi } \right) = {\sin ^2}x$$ for all real $$x$$.
Statement-1 is True, Statement-2 is True; Statement-2 is is a correct explanation for Statement-1.
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
Statement- 1 is True, Statement-2 is False.
Statement-1 is False, Statement-2 is True.