Question

sinx-tanx=0

Answer 1

Note that
\[\large \begin{aligned}\sin x - \tan x = 0 &\implies \sin x - \dfrac{\sin x}{\cos x} = 0 \\ &\implies \sin x\left(1-\frac{1}{\cos x}\right) = 0\\ &\implies \sin x = 0\quad\text{ or }\quad 1-\frac{1}{\cos x}=0\\ &\implies\sin x = 0\quad\text{ or }\quad \cos x=1\end{aligned}\] Can you take things from here? :-)

Answer 2

sinx - tanx = 0
sinx - sinx/cosx = 0
(sinx cosx - sinx)/cosx = 0

set sinx cosx - sinx = 0
sinx (cosx - 1) = 0
sinx = 0 or cosx - 1 = 0
x = k(pi) where k is integer

cosx = 1
x = turns out to be same solutions

ANSWER: x = k(pi), k is an integer