Asked by Kewal
Find all the angles between 0° and 90° which satisfy the equation
sec²Θcosec²Θ + 2cosec²Θ = 8
sec²Θcosec²Θ + 2cosec²Θ = 8
Answers
Steve
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°
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°