2csc^2(x) = 4, i need to find the solutions?

Question

okay, i guess you can get rid of 2 by dividing both sides which gives you csc^2(x) = 2 and then from there i know that 1 + cot^2(x) = csc^2(x), so i replace and get cot^2(x) = 1. but from there i don't know what to do because of the ^2. any suggestions?

Answer 1

I reckon that your problem is that your calculator does not have a csc function?

By def'n, csc(x) = 1 / sin(x)
So if csc(x) = +/- sqrt(2)
then sin(x) = +/- 1/sqrt(2)
This is a known trig relation
x = 45, 135, 225, 315 degrees, etc, etc
or π/4, 3π/4, 5π/4, 7π/4, etc, etc

Answer 2

cosec ² x = 2
1 / sin ² x = 2
sin ² x = 1 / 2
sin x = ± √(1/2)
x = 45° , 135° , 225° , 315°

Answer 3

2 csc² x = 4
csc² x = 2
csc x = ±√2
sin x = ±√2 / 2
for x in [0, 2π), x = π/4, 3π/4, 5π/4, 7π/4.

Answer 4

csc^2 x = 2
csc x = sqr(2)
x = 45 degrees

the triangle sides are 1,1, sqr(2)

Answer 5

2csc^2(x) = 4
csc^2(x) = 2
1/sin^2(x) = 2
2 sin^2(x) = 1
sin^2(x) = 1/2
sqrt [sin^2(x)] = sqrt(1/2)
sin(x) =-+ 1/sqrt(2)
x = 45 dgrees
or x = 315 dgrees