Solve the trigonometric equation 8sin(x)+5=3sin(x)

 Exercise

$8\sin\left(x\right)+5=3\sin\left(x\right)$

 

Group the terms of the equation by moving the terms that have the variable $x$ to the left side, and those that do not have it to the right side

$8\sin\left(x\right)-3\sin\left(x\right)=-5$

 

Combining like terms $8\sin\left(x\right)$ and $-3\sin\left(x\right)$

$5\sin\left(x\right)=-5$

 

Divide both sides of the equation by $5$

$\sin\left(x\right)=-\frac{5}{5}$

 

Divide $-5$ by $5$

$\sin\left(x\right)=-1$

 

This equation has no solutions in the real plane

$No solution$

$No solution$

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