Question

sin x tan x -1 = tan x - sin x​

Answer 1

$\huge\color{Black}\boxed{\colorbox{yellow}{❀Answer❀}}$

$sinx tanx - 1 = tanx - sinx \\ \implies sinx - 1 = tanx - sinxtanx \\ \implies - (1 - sinx) = tanx(1 - sinx) \\ \implies \: tanx = - 1 \\ \implies \: tanx = - tan \frac{\pi}{4} \\ \implies tanx = tan( - \frac{\pi}{4} )\\ \implies \: x = n\pi - \frac{\pi}{4} \\ where \: \: n = 1, \: \: 2 ,\: \: 3 ,\: \: 4 \: ...\\ put \: n = 1 \\ x = \pi - \frac{\pi}{4} = \frac{3\pi}{4} \\ put \: n = 2 \\ x = 2\pi - \frac{\pi}{4} = \frac{7\pi}{4} \\ hence \: \: x = \frac{3\pi}{4} , \: \: \frac{7\pi}{4} ,\: \: \frac{11\pi}{4}...$

Answer 2

Refer the attachment for the answer ✔️