SOLUTION: secx/cotx+tanx=sinx

Question 435641: secx/cotx+tanx=sinx
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
secx/cotx+tanx=sinx
Multiply thru by cot
sec + 1 = sin*cot = sin*(cos/sin) = cos
Multiply by cos
1 + cos = cos^2
cos^2 - cos - 1 = 0
Sub x for cos
x^2 - x - 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=5 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.61803398874989, -0.618033988749895. Here's your graph:

------------
cos(x) = -0.618...
x =~ 128 degs

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