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

Problem

sin(x)=cos(x)

Solution

1. Divide both sides of the equation by cos(x) assuming cos(x)≠0

sin(x)/cos(x)=cos(x)/cos(x)

2. Apply the trigonometric identity tan(x)=sin(x)/cos(x) to simplify the left side.

tan(x)=1

3. Identify the reference angle where the tangent function equals 1 which occurs at x=π/4

x=arctan(1)

4. Determine the general solution by adding the period of the tangent function, which is n*π for any integer n

x=π/4+n*π

Final Answer

sin(x)=cos(x)⇒x=π/4+n*π

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