Question

sin4x=4sinxcosxcos2x?

Answer 1

Ok.

Is it true that - sin 4x = sin(2x+2x) ?

Answer 2

yes

Answer 3

Ok chuck that.

You know that sin 2x = 2 sin x cos x ?

i.e. this half angle formula?

Answer 4

yess

Answer 5

Ok.

Then will it be true that - sin 4x = 2 sin 2x . cos 2x ?

Answer 6

yes

Answer 7

and as we saw just now that sin 2x = 2 sin x cos x

i.e. 2 sin 2x . cos 2x

=> 2 . 2 (sin x cos x) . cos 2x (since sin 2x = 2 sin x cos x)

=> 4 sin x cos x . cos 2x. is the result.

Answer 8

thank you!!