Question

Find the solutions of the equation that are in the interval [0, 2π)
tan2 x sin x = 3 sin x

Answer 1

\(\large\color{black}{ \displaystyle \tan^2x\sin x =3\sin x }\) link this ?

Answer 2

*like* this?

Answer 3

@SolomonZelman Yes!
\[(\tan ^{2} x)(\sin x) = 3 \sin x\]

Answer 4

yes, same thing:D

Answer 5

I'm not sure what to do with the tan out front...

Answer 6

\(\large\color{black}{ \displaystyle \tan^2x\sin x =3\sin x }\)

\(\large\color{black}{ \displaystyle \tan^2x\sin x -3\sin x =0}\)

\(\large\color{black}{ \displaystyle \left(\tan^2x -3\right)\sin x =0}\)

Answer 7

and the zero product property

Answer 8

@SolomonZelman That's how far I got before I got stuck.

Answer 9

@SolomonZelman
So is it \[(\tan ^{2}x -3) = 0\] and \[\sin x = 0\] ?

Answer 10

yes

Answer 11

Awesome thank you!

Answer 12

yw.