SOLUTION: Find all the angles between 0° and 90° which satisfy the equation secēΘcosecēΘ + 2cosecēΘ = 8

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Question 550771: Find all the angles between 0° and 90° which satisfy the equation
secēΘcosecēΘ + 2cosecēΘ = 8
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find all the angles between 0° and 90° which satisfy the equation
sec%5E2%28t%29%2Acsc%5E2%28t%29+%2B+2csc%5E2%28t%29+=+8
Multiply by sin^2*cos^2
1 + 2cos^2 = 8sin^2cos^2 = 8cos^2*(1 - cos^2)
1 + 2cos^2 = 8cos^2 - 8cos^4
8cos^4 - 6cos^2 + 1 = 0
Sub x = cos^2
8x^2 - 6x + 1 = 0
(2x - 1)*(4x - 1) = 0
x = 1/2, x = 1/4
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cos^2(t) = 1/4
cos^2(t) = 1/2
Can you finish it?