Question

Solve: cos² Ɵ + cos Ɵ = 1

Answer 1

use the quadratic formula to find values of cos theta

Answer 2

I don't get it, both of the answers :(

Answer 3

cos^(2)x+cosx=1

To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
cos^(2)x+cosx-1=0

Use the quadratic formula to find the solutions. In this case, the values are a=1, b=1, and c=-1.
cosx=(-b+-sqrt(b^(2)-4ac))/(2a) where acos^(2)x+bcosx+c=0

Use the standard form of the equation to find a, b, and c for this quadratic.
a=1, b=1, and c=-1

Substitute in the values of a=1, b=1, and c=-1.
cosx=(-1+-sqrt((1)^(2)-4(1)(-1)))/(2(1))

Simplify the section inside the radical.
cosx=(-1+-sqrt(5))/(2(1))

Simplify the denominator of the quadratic formula.
cosx=(-1+-sqrt(5))/(2)

First, solve the + portion of \.
cosx=(-1+sqrt(5))/(2)
-----------------------------------------
Next, solve the - portion of \.
cosx=(-1-sqrt(5))/(2)
-----------------------------------------
The final answer is the combination of both solutions.
cosx=(-1+~(5))/(2),(-1-~(5))/(2)
=============================
Set up each of the solutions to solve for x.
cosx=(-1+sqrt(5))/(2) ,cosx=(-1-sqrt(5))/(2)
----------------------------------------
Set up the equation to solve for x.
cosx=(-1+sqrt(5))/(2)

Solve the equation for x.
\[x=0.9046\pm 2\pi n,5.3786\pm 2\pi n\]
---------------------------------------
Set up the equation to solve for x.
cosx=(-1-sqrt(5))/(2)

Solve the equation for x.
Undefined for cosx=(-1-sqrt(5))/(2) but not cosx=(-1+sqrt(5))/(2)
--------------------------------------
Only solution is \[x=0.9046\pm 2\pi n,5.3786\pm 2\pi n\]