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Question

Find the integral of the function 1cos(xa)cos(xb)

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Solution

1cos(xa)cos(xb)=1sin(ab)[sin(ab)cos(xa)cos(xb)]

=1sin(ab)[sin[(xb)(xa)]cos(xa)cos(xb)]

=1sin(ab)[sin(xb)cos(xa)cos(xb)sin(xa)]cos(xa)cos(xb)

=1sin(ab)[tan(xb)tan(xa)]

1cos(xa)cos(xb)dx=1sin(ab)[tan(xb)tan(xa)]dx

=1sin(ab)[log|cos(xb)|+log|cos(xa)|]

=1sin(ab)[logcos(xa)cos(xb)]+C

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