(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

Any of the identities

3. 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.

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# A trig equation

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