Please help checking proof?

Question

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?

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Answer 1 · 2017-04-29T15:53:05

See below.

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#