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

Sagot :

Rabinshrestha41idn
I am replacing θ with A, so don't get confused

[tex]csc^{2} A-4=0[/tex]

[tex]csc^{2} A- 2^{2} =0[/tex]

[tex](cscA+2)(cscA-2)=0[/tex]

Using zero product property:
EITHER
[tex]cscA+2=0[/tex]
[tex]cscA=-2[/tex]
[tex]A = -30[/tex]°

OR
[tex]cscA-2=0[/tex]
[tex]cscA=2[/tex]
[tex]A=30[/tex]°

 
Mariamikaylaidn
[tex]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}[/tex]
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