Question

Please help
Find the specific values of x on the interval [0,2pi]
sin(2x)tan(2x)+sin(2x)=0

Answer 1

I tried converting tan to sin/cos
And then simplifying from there by converting everything into sines and multiplying, but I have no idea where to go from here

Answer 2

Umm I need to do this algebraically so I can't just go through an check them
I need to simplify the equation

Answer 3

I notice that your expression can be factored. Would you please factor it now.

Answer 4

Oh sorry I was gone
Ok so I got sin2x(tan2x+1)
Do I expand using addition properties?

Answer 5

\(\color{#000000 }{ \displaystyle ab+a=0 }\)
\(\color{#000000 }{ \displaystyle (a\times b)+(a\times 1)=0 }\)
\(\color{#000000 }{ \displaystyle a(b+1)=0 }\)

\(\color{#000000 }{ \displaystyle a=0 }\) or, \(\color{#000000 }{ \displaystyle b+1=0\quad \Longrightarrow\quad b=-1 }\)\(\small .\)

Answer 6

You are just applying the basic algebra, but to trigonometric functions, rather than just numbers.

Answer 7

Oh I see that
Lol I was thinking more complicated
Thank you!

Answer 8

Well, what you have at the moment (which is correct) is\(\small : \)
\(\color{#0000ff }{ \displaystyle \sin(2x)\left[\tan(2x)+1\right]=0}\)

Then, by the "zero property" you have\(\small : \)
\(\color{#0000ff }{ \displaystyle \sin(2x)=0\quad}\)or,\(\color{#0000ff }{ \displaystyle \quad \tan(2x)+1=0}\)

Answer 9

Yeah I got the specific solutions of 0, pi/2,pi,3pi/2,2pi,3pi/8,7pi/8,11pi/8, and 15pi/8
Is that correct?

Answer 10

\(\color{#0000ff }{ \displaystyle \sin(2x)=0\quad {\small \rm then}\quad x=0,~~\frac{\pi}{2},~~\frac{3\pi}{2},~~2\pi}\)

\(\color{#0000ff }{ \displaystyle \tan(2x)+1=0\quad {\small \rm then}\quad x=\frac{3\pi}{8},~~\frac{7\pi}{8},~~\frac{11\pi}{8},~~\frac{15\pi}{8}}\)

Answer 11

yes, your answers are all correct.

Answer 12

(I am lagging a little, sorry takes time to type it)

Answer 13

Alright thank you!

Answer 14

YW

Answer 15

the first one is for values where sin(x) and cos(x) are zero, what is the second for the double angle of the tangent