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The formulae for the sum the sine and cosine of two angles are: 2(cos x°cos 50°- sin x°sin 50°)= sin x°cos 40°+cos x°sin 40°cos 50°= sin 40°sin 50° = cos 40° Therefore, 2 cos x°sin 40°- 2 sin x°cos 40° = ...

The general formula for integration by parts to integrate something of the form u * v' is: u * v - (integral)[ (u' * v) dx ]. Thus we first need to write x * sin(...