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**reindeer7** We know cos (2x) =2cos^{2}(x) -1. Now my exercise book gives an example, asking to find cos (0.5x) if cos (x) =0.3.It says that you must replace x with 0.5x so that your new angle formula will be cos (x) =2cos^{2}(0.5x) -1.I want to know how the domain of the cos function changed on either side of the equality sign (=).What is the principle involved in changing the domain, the operations done.It seems that you just multiplied all the x`s in the whole expression with the coefficient of the x which is in the domain of the function of which you are finding the range.This sort of thing I have seen in simple algebra but how does this work in trig functions? An explanation in which you substitute the 2x or 0.5x etc in the domain with some other variable like u would be greatly appreciated.