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Recall that sin(x) = (e^ix-e^-ix)/(2i) and we can rewrite the integrand as {(e^ix-e^-ix)/(2i)}⁶Factor out {1/(2i)}⁶, which is -1/64, of the in...

Cos^2(x) + sin^2(x) = 1. Therefore Cos^2(x) = 1 - sin^2(x). So equation becomes 3Sin^2(x) + sin(x) + 8 = 9(1 - sin^2(x)). Then becomes 12sin^2(x) + sin(x) - 1This is quadratic equation, solved to (4sin(x)...

=(3x56)x⁵⁵

A stationary point implies that the gradient at this point will be equal to 0, it is a turning point in the graph. So we need to find the value of X at which dy/dx = 0. [where dy/dx is the gradient.]So we...

Recall the identity ((cos x)^2+(sin x)^ 2=1). Rearrange the identity to give cos x in terms of sin x. Substitute this into the equation. Rearrange so all terms are on one side of the equation and factorie...