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

Problem

cos(x)=sin(x)

Solution

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

sin(x)/cos(x)=1

2. Apply the trigonometric identity tan(x)=sin(x)/cos(x)

tan(x)=1

3. Determine the principal value of x by taking the arctangent of both sides.

x=arctan(1)

x=π/4

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

x=π/4+n*π

Final Answer

cos(x)=sin(x)⇒x=π/4+n*π,n∈ℤ

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