2cosx+sinx+1=0

Question

how do I get everything in one function?

Answer 1

2cosx+sinx+1=0
2cosx = -sinx-1
square both sides
4cos^2 x = sin^2 x + 2sinx +1
4(1-sin^2 x) = sin^2 x + 2sinx +1
4 - 4sin^2 x = sin^2 x + 2sinx +1
5sin^2 x + 2sinx -3 = 0
(sinx+1)(5sinx-3)=0
sinx=-1 or sinx = 3/5
x = 270 degrees or x = 36.9 degrees or 143.1 degrees.

but remember we squared, so all answers must be verified in the original equation

if x = 270
LS = 2cos 270 + sin270 + 1
= 0-1+1 = 0 = RS

if x= appr. 36.9
LS = 2cos36.9+sin36.9+1
= not the right side

so x = 270 degrees or 3pi/2 radians