prove the identity:

1) sin4x = 2sin2xcos2x

2)cos6x = 2cos^2 3x-1

3)sin3x = sin x(4cos^2 x-1)

Thank you for the opportunity to help you with your question!

1)We can prove the identity using the formula ,sin(2A)=2sinAcosA

Here A=2x

therefore,

2)cos(6x)

We have the double angle formula for cos 2A

On comparing here A=3x

Thus,

3)sin(3x)

It can be written as

sin(x+2x)

Using the sum of angle formula for sin(A+B)=sinAcosB+cosBsinA

Substitute,

Factoring out sinx

---Thanks--------

;)

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