int(cos.(x)/(2)-sin.(x)/(2))^(2)dx equal...

`int(cos.(x)/(2)-sin.(x)/(2))^(2)dx` equals

A

`x+cosx+c`

B

`2cos^2((x)/(2))+c`

C

`(1)/(3)(cos((x)/(2))-(x)/(2))^3+c`

D

`x-cosx+c`

Verified by Experts

The correct Answer is:

A

`int(cos(x)/(2)-sin(x)/(2))^(2)dx`
`=int{cos^(2)(x)/(2)+sin^(2)(x)/(2)-2sin(x)/(2)cos(x)/(2)}dx`
`=int(1-sinx)dx=x+cosx+c`

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