Solve for x tan(x)sin(x)+sin(x)=0

Problem

tan(x)*sin(x)+sin(x)=0

Solution

1. Identify the common factor in the terms of the equation.

2. Factor out the term sin(x) from the left side of the equation.

sin(x)*(tan(x)+1)=0

3. Apply the zero product property by setting each factor equal to zero.

sin(x)=0

tan(x)+1=0

4. Solve the first equation sin(x)=0 for x

x=n*π

5. Solve the second equation tan(x)=−1 for x

x=(3*π)/4+n*π

6. Combine the solutions, where n represents any integer.

Final Answer

tan(x)*sin(x)+sin(x)=0⇒x=n*π,(3*π)/4+n*π

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