Sociology homework help

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The integral/antiderivative you require is
##I = intsin(2x)/cos(x)dx##
The easiest way to solve it is to use trigonometric identities and expand the numerator, like this
##sin(2x) = 2sinxcosx##
This transforms the integral in this way
##I = int2sinxcosx/cosxdx##
##=> I = 2intsinxdx##
##=> I = -2cosx + C##