SOLUTION: Hi, I have been stuck on this part of a question for a while. I have got to the stage; 4cos^2(36) - 2cos(36) -1 = 0 of a trig. identity but need to simplify this down into the

Question 847512: Hi, I have been stuck on this part of a question for a while.
I have got to the stage;
4cos^2(36) - 2cos(36) -1 = 0 of a trig. identity but need to simplify this down into the form a+b√5 where a and b are found.
The steps to this confuse me and I don't understand how to do this.
Any help is greatly appreciated.
Thank you!!

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Hi, I have been stuck on this part of a question for a while.
I have got to the stage;
4cos^2(36) - 2cos(36) -1 = 0 of a trig. identity but need to simplify this down into the form a+b√5 where a and b are found.
==================
It's not clear what you're trying to do.
That's not an identity. It has no variable.
If it is true, you can solve for cos(36).
Sub x for cos(36)
----

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=20 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.809016994374947, -0.309016994374947. Here's your graph:

===============================

RELATED QUESTIONS
So I am in AP calc this year, and I have to do a review test, and can't find any of my... (answered by jim_thompson5910)

Hello, i have been haveing truble with this trig problem for a little while. the... (answered by jim_thompson5910)

I have been stuck on this question for a while, thanks What is the inverse of f if f(x)... (answered by MathTherapy)

Hi I am having great difficulty trying to solve the following:- I have tried puting (answered by amylouise93,jim_thompson5910)

evaluate the expression described below if the number is nine two times the difference... (answered by rwm)

Hi, I am not sure how to approach this question, any help is appreciated. Thanks!... (answered by stanbon)

Hi I have a question about a math problem on my homework. The question states: The... (answered by stanbon,rfer)

Hi there! I am not very good at math and I have been stuck on this question for 20... (answered by macston,josmiceli)

Hi! I'm stumped on the second part of this question. Could someone explain the steps for... (answered by Boreal)