SOLUTION: This problem was given with the instructions to "Verify". PLEASE explain how both sides of the equation are equal to each other. I am a little bit unclear. Would you use variations

Question 1013496: This problem was given with the instructions to "Verify". PLEASE explain how both sides of the equation are equal to each other. I am a little bit unclear. Would you use variations?
cot^2(a)= cos^2(a)+ cot(a)*cos(a)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
cot^2(a)= cos^2(a)+ cot(a)*cos(a)
cot = cos/sin
-----
cos^2/sin^2 = cos^2 + cos^2/sin
1/sin^2 = 1 + 1/sin
1 = sin^2 + sin
sin^2 + sin - 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: 0.618033988749895, -1.61803398874989. Here's your graph:

================
sin(a) =~ 0.618034
a =~ 38.17 degs (principal value)
=========================
Not an identity.

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