Question 166649
tan(x)sin(x)-sin(x)=0 ... Start with the given equation


sin(x)(tan(x)-1)=0 ... Factor out the GCF sin(x)


sin(x)=0   or tan(x)-1=0 ... Set each factor equal to zero


Solve the first equation:


sin(x)=0  ---> x = 0 + 2pi*n  ... or ... x = pi + 2pi*n



Solve the second equation:


tan(x)-1=0=0  ---> tan(x)=1 ----> x = pi/4 + pi*n


So the solutions are 


x = 0 + 2pi*n  ... or ... x = pi + 2pi*n ... or ... x = pi/4 + pi*n


where "n" is an integer.