3sin ^ 2x + 4sin xcos x - 4 cos ^ 2x = 0​

\begin{gathered}\sin^2(x)+3\sin(x)\cos(x)-4\cos^2(x)=0\Big/\div\cos^2(x)\\\tan^2(x)+3\tan(x)-4=0\\\tan(x)=u\\u^2+3u-4=0\\u_{1,2}=1;-4\\\begin{cases}\tan(x)=1\\\tan(x)=-4\end{cases}\Rightarrow\begin{cases}x=\frac{\pi}{4}+\pi k\\x=-\tan^{-1}(4)+\pi k\end{cases}, k\in \mathbb Z\end{gathered}

sin

2

(x)+3sin(x)cos(x)−4cos

2

(x)=0/÷cos

2

(x)

tan

2

(x)+3tan(x)−4=0

tan(x)=u

u

2

+3u−4=0

u

1,2

=1;−4

{

tan(x)=1

tan(x)=−4

⇒{

x=

4

π

+πk

x=−tan

−1

(4)+πk

,k∈Z

P.s тангенс в минус первой степени - это арктангенс.