Question 1064092
<font color=black size=3>{{{3*csc(x)+5 = csc(x)+9}}} Start with the given equation



{{{3*csc(x)+5-5 = csc(x)+9-5}}} Subtract 5 from both sides



{{{3*csc(x) = csc(x)+4}}} Combine like terms



{{{3*csc(x)-csc(x) = csc(x)+4-csc(x)}}} Subtract csc(x) from both sides



{{{2csc(x) = 4}}} Combine like terms



{{{(2csc(x))/2 = 4/2}}} Divide both sides by 2



{{{csc(x) = 2}}} Reduce



{{{1/(sin(x)) = 2/1}}} Rewrite csc(x) in terms of sine. Rewrite the "2" on the right side as "2/1"



{{{sin(x) = 1/2}}} Apply reciprocals to both sides



The goal now is to solve {{{sin(x) = 1/2}}} or {{{sin(theta) = 1/2}}} 



Use a <a href = "https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png">unit circle</a> to find points on the unit circle that have a y coordinate of y = 1/2. This happens at theta = 30 and theta = 150 (in Q1 and Q2 respectively)


So that means x = 30 or x = 150 (where x is the angle in degrees). 



The final answer is <font color=red>Choice A) 30 degrees and 150 degrees</font></font>