csc^2 θ − 4 = 0 find all solutions to the given equation
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
\(cscA-2=0\)
\(cscA=2\)
\(A=30\)°
\(csec^2\beta-4=0 \\\\ (csec\beta-2)(csec\beta+2)=0 \\\\\\ \#1 \\\\ csec\beta-2=0 \\\\ csec\beta=2 \\\\ \boxed{\beta=-1.099} \\\\\\ \#2 \\\\\ csec\beta+2=0 \\\\ csec\beta=-2 \\\\ \boxed{\beta=1.099}\)