Find the general solution of the equation sin x = tan x .

Explanation

Given, `sin x= tan x`
`sin x = (sin x)/(cos x)`
`rArr sin x * cos x = sin x`
`rArr sin x* cos x - sin x = 0 `
`rArr sin x(cos x-1)=0`
`rArr ` either `sin x = 0 ` or ` cos x - 1 = 0 `
`rArr ` either `sin x = 0 ` or ` cos x = 1 `
`rArr ` either ` sin x = 0 ` or `cos x = cos 0` [`:'cos0=1`]
The general solution of `sin theta = 0 `is `theta = n pi , n in Z`
and `cos theta = cos alpha ` is `theta = 2n pi pm alpha`, where `n in Z`
`:.` The required general solution is
`x=n pi ` or `x = 2n pi pm 0, n in Z`
`:.x=n pi ` or `x= 2n pi, n in Z`