# Trigonometry

posted by .

Find all the angles between 0° and 90° which satisfy the equation
sec²Θcosec²Θ + 2cosec²Θ = 8

• Trigonometry -

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°

## Similar Questions

2Sin(Θ+47°)=1 ΘЄ[0°, 360°) What I did: Sin(Θ+47°)=1/2 Sin 1/2 = Θ+47° 30°+360 = Θ+47° 343° = Θ Ok, so how do i find the other solutions?
2. ### Math-Trig

Trig Questions- 1. Write the algebraic expression which shows Cos((ArcSin(4/X)), 2. Angle If Csc(-Θ)=15/4?
3. ### math-Trig

1. Write the algebraic expression which shows Cos((ArcSin(4/X)), 2. Angle If Csc(-Θ)=15/4?
4. ### Trigonometry

1. Find the exact value of the following (Think identity) Cos(2 Arccos(5/13)) 2. Solve the following equation for 0° ≤ Θ < 360° Sec(Θ)= tan(Θ) + cos(Θ)
5. ### Trigonometry

Solve the equation cotΘ-abtanΘ = a-b Answer-tanΘ=1/a or -1/b
6. ### Trigonometry

If cospΘ + cosqΘ = o. prove that the different values of Θ form two arithmetical progressions in which the common differences are 2π/p+q and 2π/p-q respectively.
7. ### TRIGONOMETRY HELP

Prove that: cos²Θ - sin²Θ = 2cos²Θ - 1