Question

prove that:::-
$\frac{sin \: x \: - \: sin \: 3x}{ {sin}^{2}x \: - {cos}^{2}x } = 2sin \: x$
​

Answer 1

ANSWER⤵️

$:\longrightarrow\pink{LHS }</p><p></p><p>$

$: \rightarrow{\: \frac{2cos( \frac{x + 3x}{2}) \: sin( \frac{x - 3x}{2} ) }{ - ( {cos}^{2}x - {sin}^{2}x) } }$

$: \rightarrow\: \frac{2cos \: 2x \: sin( - x)}{ - cos2x}$

$: \rightarrow{\: \frac{ - 2cos2xsinx}{ - cos2x} }$

$:\longrightarrow \purple{ \: 2sin \: x}$

$:\longrightarrow \pink{RHS}$

HENCE PROVED

$\orange{BE \: \: BRÃÎÑLY❥}$

$†HOPE \: \: IT \: \: HELPS†$