SOLUTION: Find all values of x in the interval (0, 2pi) that satisfy the condition: ((csc^2)x)-1=4 (cos^2x)

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Question 941687: Find all values of x in the interval (0, 2pi) that satisfy the condition:
((csc^2)x)-1=4 (cos^2x)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find all values of x in the interval (0, 2pi) that satisfy the condition:
((csc^2)x)-1=4 (cos^2x)
***
csc%5E2%28x%29-1=4%28cos%5E2%28x%29%29
1%2Fsin%5E2%28x%29-1=4%281-sin%5E2%28x%29%29
1%2Fsin%5E2%28x%29-1=4-4sin%5E2%28x%29%29
1%2Fsin%5E2%28x%29=5-4sin%5E2%28x%29%29
4sin%5E2%28x%29%2B%281%2Fsin%5E2%28x%29%29-5=0
lcd:sin^2(x)
4sin%5E4%28x%29%2B1-5sin%5E2%28x%29=0
4sin%5E4%28x%29-5sin%5E2%28x%29%2B1=0
(4sin^2(x)-1)(sin^2(x)-1)=0
..
4sin^2(x)-1=0
sin^2(x)=1/4
sin(x)=±1/2
x=π/6,5π/6,7π/6,11π/6
or
sin^2(x)=1
sin(x)=±1
x=π/2,3π/2