Question

How do you solve `9sin^2xtanx=16tanx`?

Answer 1

`color(green)(x=k*pi " for " k in ZZ)`

Explanation:

Given
`color(white)("XXX")color(red)(9sin^2x) * color(blue)(tan x) = color(red)(16) * color(blue)(tan x)`

`rArr`
`{:(tan x=0,color(white)("X")orcolor(white)("X"),9sin^2 x =16), (rarr x in {0, pi, 2pi,...},,sin^2 x =16/9), (,,sin x = +- 4/3), (,,"impossible: " sin x in [-1,+1]) :}`