how do i solve this? i'm suppose for solve x
(Cotx)(Cosx)= Cosx
$\displaystyle cot(x)~cos(x) = cos(x)$
$\displaystyle cot(x)~cos(x) - cos(x) = 0$
$\displaystyle (cot(x) - 1)~cos(x) = 0$
So either
$\displaystyle cot(x) - 1 = 0 \implies tan(x) = 1 \implies x = \frac{\pi}{4}, \frac{5\pi}{4}$
or
$\displaystyle cos(x) = 0 \implies x = \frac{\pi}{2}, \frac{3\pi}{2}$
-Dan
umm...i suppose you just want us to factor this.
tan(x) is common to the first two terms, 5 is common to the last two, so pull those out, we get:
$\displaystyle \tan x (4 \sin x - 3) + 5 (4 \sin x - 3)$
now the 4sin(x) - 3 is common to both terms, so pull that out, we get:
$\displaystyle (4 \sin x - 3)( \tan x + 5)$
and we're done
Aside: post new questions in a new thread