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

Problem

cos(x)−sin(x)=0

Solution

1. Rearrange the equation by adding sin(x) to both sides to isolate the trigonometric terms.

cos(x)=sin(x)

2. Divide both sides by cos(x) assuming cos(x)≠0 to express the equation in terms of the tangent function.

sin(x)/cos(x)=1

3. Substitute the identity tan(x)=sin(x)/cos(x) into the equation.

tan(x)=1

4. Determine the general solution for x by finding the values where the tangent is 1 which occurs at π/4 plus any integer multiple of the period π

x=π/4+n*π

Final Answer

cos(x)−sin(x)=0⇒x=π/4+n*π,n∈ℤ

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