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प्रश्न
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
उत्तर
`int((cos2x - cos2 alpha)/(cosx - cos alpha)) "d"x`
= `int [((2 cos^2x - 1) - (2cos^2alpha - 1))/(cosx - cosalpha)]* "d"x`
cos 2x = cos2x – sin2x – 1
cos 2x = 2 cos2x – 1
= `int (2cos^2x - 1 - 2cos^2alpha + 1)/(cosx - cosalpha) * "d"x`
= `int (2cos^x - 2cos^2alpha)/(cosx - cosalpha) * "d"x`
= `int (2(cos^2x - cos^2alpha))/(cosx - cosalpha) * "d"x`
= `2 int [((cosx + cosalpha)(cosx - cosalpha))/(cosx - cosalpha)] * "d"x`
= `2 int(cosx + cosalpha) "d"x`
= `2 int cos x "d"x + 2 int cos alpha "d"x`
= `2 int cos x "d"x + 2 int cos alpha int "d"x`
= 2 sin x + 2 cos α(x) + c
= 2 sin x + 2x cos α + c
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