Suppose that 0<c<pi/2. For what value of c is the area of the region enclosed by the curves y = cos(x), y = cos(x-c), and x = 0 equal to the area of the region enclosed by the curves y = cos(x-c), x = pi and y = 0?

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You need to evaluate the area of the region enclosed by the curves y = cos x, y = cos(x - c) and x = 0, such that:

`A_1 = int_0^(c/2) (cos x - cos (x - c)) dx`

`A_1 = int_0^(c/2) (cos x) dx - int_0^(c/2) (cos (x - c)) dx`

`A_1 = sin x|_0^(c/2) - sin (x - c)|_0^(c/2)`

`A_1 = sin (c/2) - sin 0 - sin (c/2 - c) + sin (0 -c)`

`A_1 = sin (c/2) -sin(-c/2) + sin(-c)`

Since sin(-x) = -sin x:

`A = sin (c/2) + sin (c/2) - sin c`

`A =...

(The entire section contains 261 words.)

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