2 sin x = tan x (in degrees)?

Question

I know the answers (0, +/-60 and +/-180)...but i don't know the working. Can anybody help?

I know the answers (0, +/-60 and +/-180)...but i don't know the working. Can anybody help? By the way, the range of x is between -180 deg to 180 deg.

Answer 1

2sinx = tan x
2sinx = sin x/ cos x
cross multiply ...........
2sin x cos x= sin x
take sin x to the other side
2 sin x cos x - sin x = 0
now take out sin x

sin x (2 cos x -1) = 0

sin x = 0
so, x =0, 180 , 360
or
2cos x -1= 0
cos x = 1/2
x = 60, 360-60
x = 60 , 300

and thats the answer
oaky then hope i helped u

Answer 2

2sinx = tanx
2sinx = sinx/cosx
sinx = 0 or cosx = 1/2
(x=0 or x=+-180) or x=+-60

Answer 3

have condition to make tagx be meanful :cosx different 0(1)
2sinx = tan x
2sinx - tanx =0
2sinx -sinx/cosx =0
(2sinxcosx -sinx )/cosx=0
2sinxcosx-sinx=0( because the condition (1))
sinx(2cosx-1)=0
sinx=0 or 2cosx-1 =0
- sinx=0 x=0 and x=+/-180
- 2cosx-1=0
cosx= 1/2 x=+/-60

conclude: equation have roots :........
(i think u ve to think carefully about equation before asking , dont be lazy ! good luck.)

Answer 4

2 sinx. - sin x / cos x = 0
sin x.(2 - 1 / cos x) = 0
sin x = 0 , cos x = 1 / 2
x = 0°, 180° , 60° , 300°

Answer 5

2sinx=tanx...now tanx=sinx/cosx
2sinx=sinx/cosx....now cross multiply by cosx
2sinxcosx=sinx...now shift everything on one side
2sinxcosx-sinx=0.....now factorise
sinx(2cosx-1)=0
sinx=0 or cosx=0.5
x=0,180,360 for sinx=0
x=60,300 for cosx=0.5
Answers are 0,60,180,300,360.