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Solve for x: 0⁰ < x< 360⁰ <img src="https://tex.z-dn.net/?f=1%20%2B%205%20%5Csin%28x%20-%2010%20%7B0%7D%5E%7B0%7D%20%29

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Step-by-step explanation:

We are given a trigonometric equation and we need to find out the value of x. The angle x lies between 0° and 360° . That is ,

$\rm\implies\red{ 0^0 < x < 360^0 }$

Given trigonometric equation :-

$\rm\implies\red{ 1 + 5 sin (x-100^0)=0 }$

Subtracting 1 both sides , we have ,

$\rm\implies 5sin( x - 100^0)= -1$

Divide both sides by 5 ,

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This equation can be written as ,

$\rm\implies x - 100^0 =sin^{-1}\bigg(\dfrac{ -1}{5}\bigg) \\\\\rm\implies x - 100^0 = -11.53^0 \\\\\rm\implies x = 100^0-11.53^0\\\\\rm\implies\boxed{\bf x = 88.463^0}$

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