Question

2-cos2x=3sinx.cosx find tanx?​

Answer 1

$\bold {\huge {\mathfrak{Hello!}}}$

$2 - cos2x = 3sinx \: cosx$

$\longrightarrow \: 2 - {cos}^{2} x + {sin}^{2} x = 3sinx \: cosx$

$\longrightarrow \: {2}{ {sec}^{2} x} - 1 + {tan}^{2} x = 3 \: tanx \: \: \: \: \bold{[multiply \: \frac{1}{ {cos}^{2}x } \: both \: side}]$

$\longrightarrow \: 2 + {2}{ {tan}^{2} x} - 1 + {tan}^{2} x = 3 \: tanx$

$\longrightarrow3 \: { \tan}^{2} x - 3tanx + 1 = 0$

$\longrightarrow { \tan}^{2} x = \frac{ - ( - 3) ± \sqrt{ {( - 3)}^{2} - 4 \times 3 \times 1 } }{2}$

You can see

$\sqrt{ {( - 3)}^{2} - 4 \times 3} \leqslant 0$