sinx tanx =sinxI need help

TLDR: x= 0, pi/4 + npi, where n= any integer

This mathematical problem is an interesting concept; two terms, both equal to each other, exist on both sides; however, one of them has a variable coefficient. Believe it or not, tan(x) operates as a coefficient for sin(x) in this problem.

There are two options for this: tan(x) must equal 1, or tan(x) AND sin(x) must equal zero at the same time.

In the first situation, tan(x) doesn’t change the value of sin(x), so it simplifies to sin(x)=sin(x).

In the second situation, tan(x) would equal zero, and sin(x) would equal zero, so both sides of the equation would simplify to 0=0.

When x= 0, both sin(x) and tan(x) equal zero, so this is a solution for this problem, but it’s not the only one. If x= pi/4, tan=1. This means that pi/4 is also a solution, but so is every other solution following the repetition of the function. So, the solutions are:

X= 0, pi/4 + npi, where n= any integer.

I know the second part is confusing, but I hope this helps!