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Let F(x) be an indefinite integral of si...

Let F(x) be an indefinite integral of `sin^(2)x`
Statement I The function F(x) satisfies `F(x+pi)=F(x)` for all real x.
Because
Statement II `sin^(2)(x+pi)=sin^(2)x,` for all real x.

A

Statement - 1 True , Statement -2 is True , Statement -2 is a correct explanation for Statement -1.

B

Statement - 1 is True , Statement -2 is True , Statement -2 is a correct explanation for Statement -1.

C

Statement - 1 True ,Statement - 2 is False.

D

Statement - 1 is False , Statement - 2 is True.

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the two statements regarding the function \( F(x) \), which is an indefinite integral of \( \sin^2 x \). ### Step 1: Find the indefinite integral of \( \sin^2 x \) We know that: \[ \sin^2 x = \frac{1 - \cos(2x)}{2} \] ...
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