Question

Can anyone explain this part:

$2sin3xcos2x -6sinxcos2x-2sin3x+6sinx$
= sin5x - 5sin3x + 10sinx ​

Answer 1

Step-by-step explanation:

we know that

2sinacosb = sin(a+b) + sin(a-b)

2sin3xcos2x - 6sinxcos2x - 2sin3x + 6sinx

= 2sin3xcos2x - 3×2sinxcos2x - 2sin3x + 6sinx

= sin(3x+2x) + sin(3x-2x) - 3{sin(x+2x) + sin(x-2x) - 2sin3x + 6sinx

= sin5x + sinx - 3 {sin3x + sin(-x)} - 2sin3x + 6sinx

= sin5x + sinx - 3 (sin3x - sinx) - 2sin3x + 6sinx

||( sin(-a) = - sina)

= sin5x + sinx - 3sin3x + 3sinx - 2sin3x + 6sinx

= sin5x - 5sin3x + 10sinx