Solve Cosine Equation
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.