Solve by Factoring cos(x)=sin(x)

Problem

cos(x)=sin(x)

Solution

1. Rearrange the equation to one side by subtracting sin(x) from both sides to set the equation to zero.

cos(x)−sin(x)=0

2. Divide both sides by cos(x) assuming cos(x)≠0 to transform the equation into a single trigonometric function.

cos(x)/cos(x)−sin(x)/cos(x)=0

3. Simplify the expression using the identity tan(x)=sin(x)/cos(x)

1−tan(x)=0

4. Isolate the tangent function by adding tan(x) to both sides.

tan(x)=1

5. Solve for x by identifying the angles where the tangent value is 1 within the standard interval [0,2*π)

x=π/4,(5*π)/4

6. Generalize the solution by adding multiples of the period of tangent, which is π

x=π/4+n*π

Final Answer

cos(x)=sin(x)⇒x=π/4+n*π

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