# A trig equation

## Homework Statement

Find all solutions of the equation (tanx + sqrt(3))(cosx+2)=0

## Homework Equations

Any of the identities

## The Attempt at a Solution

(tanx + sqrt(3))(cosx + 2)=0
tan(x)cos(x)+2tan(x) + sqrt(3)cos(x) + 2sqrt(3) = 0
(sin(x)/cos(x))cos(x) + 2tan(x) + sqrt(3)cos(x) + 2sqrt(3) = 0
sin(x) + 2tan(x) + sqrt(3)cos(x) + 2 sqrt(3) = 0
sin^2(x) + 4tan^2(x) + 3cos^2(x) + 12 = 0 (square)
sin^2(x) + cos^2(x) + 2cos^2(x) + 4tan^2(x) + 12 = 0
2cos^2(x) + 4tan^2(x) + 13 = 0
cos^2(x) + 2tan^2(x) + 6.5 = 0 (Divide by 2)
1 - sin^2(x) + 2tan^2(x) + 6.5 = 0 (sin^2(x) + cos^2(x) = 1; cos^2(x) = 1 - sin^2(x))
-sin^2(x) + 2tan^2(x) + 7.5 = 0
-1 + 2sin^2(x) + 7.5/sin^2(x) (Multiply by sin^2(x))
2sin^2(x) + (6.5 + sin^2(x) + cos^2(x))/sin^2(x) -1 = 0
2sin^2(x) + 6.5 - 1 + cos^2(x) = 0
sin^2(x) + sin^2 (x) + cos^2(x) + 5.5 = 0
sin^2(x) + 6.5 = 0
sin(x) + sqrt(6.5) = 0
sin(x) = -sqrt(6.5)

The book gives an answer of -(pi/3) + k(pi), which I'd think is correct over my equations - I honestly don't know how to get to an answer because the book is horrid at teaching and I'm out of school for a bit so I can't ask the teacher for help.

I didn't really look at your work too closely, but this way seems more obvious to me.

(tan(x) + sqrt(3))(cos(x) + 2) = 0

This is equation is factored, i.e. in the form you need to solve the problem.

Therefore, this equation equals 0 when:
1) tan(x) + sqrt(3) = 0
or
2) cos(x) + 2 = 0

1) check values of 'x' for which
tan(x) = -sqrt(3)
is true
*can you solve for x?*

2) check values of 'x' for which
cos(x) = -2
is true
*can you sovle for x?*

ey body, u can do this pretty simply,

(tanx + sqrt(3))(cosx+2)=0

when this is zero?

it is zero when (tanx + sqrt(3))=0 or (cosx+2)=0, or both of them are zero, so what u have to do is just solve these two equations now, and find the overall answer.

sorry, chaotic allready stated this. i did not see it

HallsofIvy
Homework Helper
I guarentee that if you put "Solve (x- 3)(x- 5)= 0" on a basic algebra test, 1/3 of the students will multiply it out and use the quadratic formula to solve x2- 8x+ 15= 0!

symbolipoint
Homework Helper