Solve for x cos(2x)cos(x)-sin(2x)sin(x)=0

Problem

cos(2*x)*cos(x)−sin(2*x)*sin(x)=0

Solution

1. Identify the trigonometric identity for the cosine of a sum, which states cos(A+B)=cos(A)*cos(B)−sin(A)*sin(B)

2. Apply the formula to the left side of the equation by setting A=2*x and B=x

3. Simplify the expression inside the cosine function.

cos(2*x+x)=0

cos(3*x)=0

4. Solve for the argument 3*x by identifying where the cosine function equals zero.

3*x=π/2+n*π

5. Isolate x by dividing the entire expression by 3 where n is any integer.

x=π/6+(n*π)/3

Final Answer

cos(2*x)*cos(x)−sin(2*x)*sin(x)=0⇒x=π/6+(n*π)/3

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