Question

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

Answer 1

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

Answer 2

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
$cscA-2=0$
$cscA=2$
$A=30$°