Question

Solve:

$3{\sin }^{2}x-7sinx+2=0$

Answer 1

Let $u=sin\left(x\right)$.Substitute u for all occurrences of$sin\left(x\right)$.

$3u^2-7u+2$

$3u^2-6u-1u+2$

$3u(u-2)-1(u-2)$

$(u-2)(3u-1)$

Replace all occurrences of $u$ with $sin\left(x\right).$

$\left(sin\right(x)-2)\left(3sin\right(x)-1)$

Replace the leftside with the factored expression.

$\left(sin\right(x)-2)\left(3sin\right(x)-1)=0$

If any individual factor on the left side of the equation is equal to 0,the entire expression will be equal to 0.

$sin\left(x\right)-2=0$ or $3sin\left(x\right)-1=0$

$\therefore sin\left(x\right)=2$ or $sin\left(x\right)=\frac{1}{3}$