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

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

secēΘcosecēΘ + 2cosecēΘ = 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°

## Answer this Question

## Related Questions

- please - Given tan Θ = - 8/5 and sin Θ < 0, find sin Θ, cos &#...
- math-Trig - 1. Write the algebraic expression which shows Cos((ArcSin(4/X)), 2...
- Trigonometry - 1. Find the exact value of the following (Think identity) Cos(2 ...
- Math-Trig - Trig Questions- 1. Write the algebraic expression which shows Cos((...
- probability - Theoretical properties Let Θ be an estimator of a random ...
- Probability - Let Θ1 and Θ2 be some unobserved Bernoulli random ...
- Trigonometry - Solve the equation cotΘ-abtanΘ = a-b Answer-tanΘ=1...
- Trig - Identies/equation, please help! - 2Sin(Θ+47°)=1 ΘЄ[0°, ...
- TRIGONOMETRY HELP - Prove that: cosēΘ - sinēΘ = 2cosēΘ - 1
- Trigonometry - Solve the equations secΘ - 1 = (√2 - 1)tanΘ