Question

If x = 300 , then verify that sin 3 x = 3 sin x – 4 sin3 x​

Answer 1

Answer:

Step-by-step explanation:

Given,

x = 300°

To Verify :-

$sin3x=3sinx-4sin^3x$

Solution :-

Finding value of L.H.S :-

= sin3x

= sin3(300°)

= sin900°

= sin(810° + 90°)

= cos(90°)

= 0

∴ sin3x = 0

Finding value of R.H.S :-

= 3sinx - 4sin³x

= 3sin300° - 4(sin300°)³

= 3sin(360° - 60°) - 4[sin(360° - 60°)]³

= 3(-sin60°) -4(-sin60°)³

= 3(-√3/2) - 4[(-√3/2)³]

= -3√3/2 -4(-3√3/8)

= -3√3/2 + 12√3/8

= -12√3/8 + 12√3/8

= -12√3 + 12√3/8

= 0/8

= 0

∴ 3sinx - 4sin³x = 0

∴ sin3x = 3sinx - 4sin³x

0 = 0

Hence Verified.