Statement-I: The sine and cosine curves intersect infinitely many times, bounding regions of equal areas.Statement-II : The area of the figure bounded by the curves y = cos x and y = sin x and the ordinates x = 0 and x=π4is 2-1sq. units.Which of the above statement is correct.

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Statement-I: The sine and cosine curves intersect infinitely many times, bounding regions of equal areas.

Statement-II : The area of the figure bounded by the curves y = cos x and y = sin x and the ordinates x = 0 and $x = \frac{π}{4}$ is $\sqrt{2} - 1$ sq. units.

Which of the above statement is correct.

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only II

Neither I nor II

only I

Both I and II

answer is C.

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Detailed Solution

The sine and cosine curves intersect infinitely many times, bounding regions of equal areas

: The area of the figure bounded by the curves y = cos x and y = sin x and the ordinates x = 0 and $x = \frac{π}{4}$

$\int_{0}^{\frac{π}{4}} (\cos x - \sin x) d x = {(\sin x + \cos x)}_{0}^{\frac{π}{4}} = (\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}) - (0 + 1) = \sqrt{2} - 1$