Question

please solve this trigonometry question

Q.
Prove that :

Sin x + Sin 3x+ Sin 5x +Sin 7x= 4cos x cos 2x sin4x

Please solve this...☑

Answer 1

$\mathfrak{HELLO\:\: DEAR,} \\ \\ \mathit{PROVE\:\:THAT:-} \\ \\ \mathit{sinx + sin3x + sin5x + sin7x = 4cosx*cos2x*sin4x}\\ \\\mathit{\underline{NOW,}}\\ \\ \mathit{(sin7x + sinx) + (sin5x + sin3x)}\\ \\ \mathit{[2sin\frac{x + 7x}{2}*cos\frac{7x - x}{2}] + [sin\frac{5x + 3x}{2} *cos\frac{5x - 3x}{2}]}\\ \\ \mathit{[2sin4x*cos3x + 2sin4x*cosx]}\\ \\ \mathit{2sin4x[cos3x + cosx]}\\ \\ \mathit{2sin4x[2cos\frac{3x + x}{2} * cos\frac{3x - x}{2}]}\\ \\ \mathit{2sin4x[2cos2x*cosx]}\\ \\ \mathit{4sin4x*cos2x*cosx}\\ \\ \\ \large{ \mathbf{\underline{I \:\:HOPE\:\: IT'S\:\: HELP\:\: YOU\:\: DEAR,\:\: THANKS}}}$