Question

solve for [0,2pi): 3sin^2x-6sinx=0

Answer 1

Given the equation :

$3\sin ^2x-6\sin x=0$

Let: y = sin x

So,

$\sin ^2x=y^2$

the given equation will be:

$3y^2-6y=0$

Solve for y, take 3y as a common:

$\begin{gathered} 3y(y-2)=0 \\ 3y=0\rightarrow y=0 \\ y-2=0\rightarrow y=2 \end{gathered}$

so,

$\begin{gathered} y=0\rightarrow\sin x=0\rightarrow x=0or\pi \\ y=2\rightarrow\sin x=2 \end{gathered}$

Note: the range of sine function is [ -1, 1]

So, sin x = 2 ( is rejected)

So, the answer will be: x ={ 0 , pi }