Question

csc^2 θ − 4 = 0 find all solutions to the given equation

Answer 1

I am replacing θ with A, so don't get confused


`csc^(2) A-4=0`


`csc^(2) A- 2^(2) =0`


`(cscA+2)(cscA-2)=0`

Using zero product property:
EITHER

`cscA+2=0`

`cscA=-2`

`A = -30`°

OR

`cscA-2=0`

`cscA=2`

`A=30`°

Answer 2

`csec^2\beta-4=0 \\\\ (csec\beta-2)(csec\beta+2)=0 \\\\\\ \#1 \\\\ csec\beta-2=0 \\\\ csec\beta=2 \\\\ \boxed{\beta=-1.099} \\\\\\ \#2 \\\\\ csec\beta+2=0 \\\\ csec\beta=-2 \\\\ \boxed{\beta=1.099}`