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

Problem

sin(x)−cos(x)=0

Solution

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

sin(x)=cos(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. Find the general solution for x by identifying the angle whose tangent is 1 The principal value is π/4 and the tangent function has a period of π

x=π/4+n*π

Final Answer

sin(x)−cos(x)=0⇒x=π/4+n*π,n∈ℤ

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