# How do you solve this equation: csc^4 2(u)-4=0 ?

##
i use the inverse that is sin?

i use the inverse that is sin?

##### 2 Answers

Given

Factor as

To find the values where the above equation is true, we must set both factors equal to 0:

Substitute

Add two to both sides of the first equation and subtract 2 from both sides of the second equation:

Invert both sides of both equations:

Take the square root of both sides of both equations:

Take the inverse sine of both sides:

The first equation is well known but the second equation becomes the inverse hyperbolic sine:

It will be periodic at integer multiples of

Divide by 2:

#### Explanation:

Trig table and unit circle give 4 solutions:

1.

a.

b.

2.

a.

b.