SOLUTION: Solve cosec 2θ=secθ+cotθ

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Question 624676: Solve cosec 2θ=secθ+cotθ
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Solve cosec 2θ=secθ+cotθ
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csc(2t) = sec(t) + cot(t)
1/sin(2t) = 1/cos(t) + cos(t)/sin(t)
1/(2sin*cos) = 1/cos + cos/sin
1/2 = sin + cos^2
1/2 = sin + (1 - sin^2)
2sin^2 - 2sin - 1 = 0
2x^2 - 2x - 1 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=12 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.366025403784439, -1.36602540378444. Here's your graph:

sin(t) = x =~ 0.36603
theta =~ 21.47 degs (principal value)


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