Question

Solve on the interval 0,2pi) 2cscx-3=-5

Answer 1

We have that

2cscx-3=-5---------> 2cscx=-5+3---------> cscx=-2/2---------> cscx=-1

we know that
csc x=1/sin x
then
1/sin x=-1--------------> sin x=-1
x=arcsin (-1)---------> x=-90°
x=-90°---------------> 360°-90°-----------> x=270°------------> 3pi/2

the answer is
x=3pi/2 radians