Solve for x sin(x)=tan(x)

Problem

sin(x)=tan(x)

Solution

1. Rewrite the tangent function using the identity tan(x)=sin(x)/cos(x)

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

2. Subtract the right side from the left side to set the equation to zero.

sin(x)−sin(x)/cos(x)=0

3. Factor out the common term sin(x)

sin(x)*(1−1/cos(x))=0

4. Apply the zero product property to find the first set of solutions by setting the first factor to zero.

sin(x)=0

x=n*π

5. Apply the zero product property to the second factor to find the remaining solutions.

1−1/cos(x)=0

1=1/cos(x)

cos(x)=1

x=2*n*π

6. Combine the solutions. Since 2*n*π is a subset of n*π the general solution is n*π Note that tan(x) is defined for these values because cos(n*π)≠0

Final Answer

sin(x)=tan(x)⇒x=n*π

Want more problems? Check here!