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The key to solving this equation is realizing that sin(2x) can be written in terms of sin(x) and cos(x) using a double-angle formula . (With trigonometric problems similar to this one, you should always chec...

If the details of the distribution - its mean and standard deviation are known, the following transformation applies Z = (X - mean) / stdev where Z is now a random variable distributed as normal(0, 1). Now, ...

From the rules of logarithms, we know that: log(A) - log(B) = log(A/B) and thus: log(1-x) - log(x) = log[(1-x)/x] Therefore from the question, we know: log[(1-x)/x] = 1 If we then take both sides of the equa...

This question is an example of the chain rule for differentiating. Firstly, identify the inner function. In this case, it is x 2 - 3x. This function must be differentiated first: d/dx (x 2 - 3x) = 2x - 3 Sec...

As with any question involving sines and cosines, consider complex numbers as a likely way to find the answer. For this particular kind of question, where sin/cos of a multiple of x is needed in terms of sin...