The area between the curves `y=sin x and y=cos x` bounded by the lines `x=0 and x = pi//2` is

Options

A. `sqrt2-1`
B. 0
C. `2(sqrt3-1)`
D. `2(sqrt2-1)`

Answer

To find the area between the curves \( y = \sin x \) and \( y = \cos x \) bounded by the lines \( x = 0 \) and \( x = \frac{\pi}{2} \), we can follow these steps:

### Step 1: Determine the points of intersection
We need to find where \( \sin x = \cos x \) within the interval \( [0, \frac{\pi}{2}] \).

\[ \sin x = \cos x \implies \tan x = 1 \implies x = \frac{\pi}{4} \]