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Solve Cosine Equation

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How do you solve:. CosXcos4X = cos2Xcos3X

To solve the equation, you can start by using the identity cos(a)cos(b) = (cos(a+b) + cos(a-b))/2.

So, cosXcos4X = (cos(X+4X) + cos(X-4X))/2 = (cos5X + cos(-3X))/2

and cos2Xcos3X = (cos(2X+3X) + cos(2X-3X))/2 = (cos5X + cos(-X))/2

then you get (cos5X + cos(-3X))/2 = (cos5X + cos(-X))/2

then you can combine the cos5X terms cos(-3X) = cos(-X)

so you can now say that -3X = -X + 2nPi

then you can solve for X, where n is any integer X = (2nPi)/4 = n*Pi/2

So, the solutions of the equation are X = n*Pi/2, where n is any integer.