Question

sin x ×sin(60+x) ×sin(60-x)
what is the value given above​

Answer 1

Step-by-step explanation:

Sinx.sin(60-x).sin(60+x)

= sinx [ cos( 60 - x - 60 - x) - cos ( 60 - x + 60+ x ) /2

= sinx [ cos ( -2x ) - cos ( 120 ) ] /2

= sinx [ cos2x + 1/2 ] /2

= sinx [ ( 1 - 2sin²x) + 1/2 ] /2

= sinx [ 3/2 - 2sin²x ] / 2

= 3 sinx/4 - 2 sin³x /2

= 3sinx - 4sin³x / 4

= 1/4 ( sin3x )

Hope helped!

Formulae : sin3x = 3sinx - 4sin³x

2sinA* sinB = cos (A - B) - cos ( A + B)