Posted by **Kewal** on Wednesday, December 28, 2011 at 11:06pm.

Find all the angles between 0° and 90° which satisfy the equation

sec²Θcosec²Θ + 2cosec²Θ = 8

- Trigonometry -
**Steve**, Thursday, December 29, 2011 at 12:03am
multiply by sin^2 cos^2 to get

1 + 2 cos^2 = 8 sin^2 cos^2

8cos^4 - 6cos^2 + 1 = 0

(4cos^2 - 1)(2 cos^2 - 1)

so,

cos^2 = 1/4 or 1/2

cos = 1/2 or -1/2 or 1/√2 or -1/√2

skip the negative values, since we want 1st quadrant angles only

Θ = 45° or 60°

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