Respuesta :

[tex]\bf 5sin(2x)=3cos(x)\qquad \qquad sin(2\theta)=2sin(\theta)cos(\theta)\qquad thus \\\\ 5[2sin(x)cos(x)]=3cos(x)\implies 10sin(x)cos(x)=3cos(x) \\\\ 10sin(x)cos(x)-3cos(x)=0\impliedby \textit{taking common factor} \\\\\\ cos(x)[10sin(x)-3]=0\implies \begin{cases} cos(x)=0\to &\measuredangle x=cos^{-1}(0) \\\\ sin(x)=\frac{3}{10}\to &\measuredangle x = sin^{-1}\left( \frac{3}{10} \right) \end{cases}[/tex]
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Answer:

x = 17.46° or x = 90°

Step-by-step explanation:

We need to solve 5sin2x=3cosx

sin2x =

Substituting

[tex]5\times 2sinx cosx = 3 cosx\\\\cosx(10sinx-3)=0\\\\sinx=0.3\texttt{ or }cosx=0\\\\x=17.46^0\texttt{ or }x=90^0[/tex]

x = 17.46° or x = 90°

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