Option C: 90° is the value of x.
Explanation:
The given expression is [tex]4+2 \sin x=14-8 \sin x[/tex] for [tex]0^{\circ} \leq x \leq 180^{\circ}[/tex]
We need to solve the expression.
Thus, we have,
[tex]4+2 \sin x=14-8 \sin x[/tex]
Subtracting both sides by 4, we have,
[tex]2 \sin x=10-8 \sin x[/tex]
Adding both sides by 8 sin x, we get,
[tex]10 \sin x=10[/tex]
Dividing both sides by 10, we have,
[tex]sin \ x=1[/tex]
Taking [tex]sin^{-1}[/tex] on both sides of the equation, we get,
[tex]x=sin^{-1}(1)[/tex]
[tex]x=90^{\circ}[/tex]
Thus, the value of x is 90°
Hence, Option C is the correct answer.
