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We first want to get every term in terms of the same variable, namely sin(x). to do so, we will use the identity sin^2(x) +cos^2(x) = 1 to get: 4(1-sin^2(x)) -15sin(x) -13 = 0. which we can then rewrite a...

By taking the natural log on both sides we can see that: ln(f(x)) = ln(x)^2 This is a more familiar expression that we know how to differentiate  LHS: f '(x)/f(x), RHS: 2*ln(x)/x By re...

We first consider 1/z=(cosx+isinx)^(-1). Application of De Moivre's theorem for integer n: (cosx+isinx)^(n)=cosnx+isinnx yields the result 1/z=cosx-isinx. Addition of the two forms z and z^(-1) steers us ...