Question

what is the formula of sin4x

Answer 1

4sinx cos x (cos x- sinx )( cos x+ sinx)

Answer 2

The formula of sin 4x is as follows:

• The basic trigonometric formulas can be used to calculate the value of sin4x.

• To obtain the values of sin4x, we'll apply fundamental trigonometric formulas.

We can write sin4x in a simpler way

Sin4x= sin2(2x)

We have sin2x = sin2xcos2x

Putting the value of sin2x

We will get, sin2(2x) = 2sin2xcos2x

= 2 (2 sinx cosx) cos2x

We know that, cos2x = 2cos2x - 1

Putting the value of cos2x in the formula:

Sin2(2x)= 4 sinx cosx (2cos2x - 1)

= 8 sinx cos3x - 4 sinx cosx

Sin 4x = 8 sinx cos3x - 4 sinx cosx

Hence, the formula of sin 4x is 8sinxcos3x-4sinxcosx.