Question

Please help checking proof?

Here is my proof, which is wrong?

I am proving sinx - sinxtanx =0
sinx = sinxtanx
1 = tanx

Apparently I HAVE to factor out sinx. Why is that?

Answer 1

See below.

Explanation:

If you have

`f(x)=sinx-sinx tanx`

and do you want to know for what set of values in `x`

`f(x) = 0`

then you must consider the equation

`sinx-sinx tanx=0`

or

`sinx(1-tanx)=0`

because there are distinct values that obey the condition

`{(sinx=0),(1+tanx=0):}->{(x = k pi),(x=-pi/4 + k pi):}`

so the total set is

`x = (k pi) uu (-pi/4 + k pi)` with `k in ZZ`