Question

.
Find the general solution of sin x = tan X.​

Answer 1

Answer:

Step-by-step explanation:

sin θ = 0 implies θ = nπ and cos θ = cos α implies θ = 2nπ±α , n ∈ Z. ∴ the required general solution is x = nπ or x = 2mπ, where n, m ∈ Z.

Answer 2

$\sin(x) = \tan(x) \\ \\ \sin(x) = \frac{ \sin(x) }{ \cos(x) } \\ \\ \sin(x) \cos(x) - \sin(x) = 0 \\ \\ \sin(x) ( \cos(x) - 1)=0 \\ \\ \sin(x) = 0 \: or \: \cos(x ) = 1 \\ \\ \sin(x) = \sin(0) \: or \: \cos(x) = \cos(0)$

$\bf{Since\: , sin \theta=0 \:implies \:\theta=n\pi \:and \: cos \theta=cos \alpha \:implies \: \theta=2n \pi \pm \alpha , n \in Z}$

$\bf{x=n \pi, \: x=2m \pi \pm 0}$

The required general solution is

$\bf{x = n\pi \: or \: x = 2m \pi \: where \: n \: , \: m \: \in Z}$