Question 941687
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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{{{csc^2(x)-1=4(cos^2(x))}}}
{{{1/sin^2(x)-1=4(1-sin^2(x))}}}
{{{1/sin^2(x)-1=4-4sin^2(x))}}}
{{{1/sin^2(x)=5-4sin^2(x))}}}
{{{4sin^2(x)+(1/sin^2(x))-5=0}}}
lcd:sin^2(x)
{{{4sin^4(x)+1-5sin^2(x)=0}}}
{{{4sin^4(x)-5sin^2(x)+1=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