how can 3sin2x becomes 3(2 sinx kos x)?

Question

i need help with these kind of question.Pls help me

Answer 1

Sin 2x = 2 sinx cos x

This can be derived from formula for sin (A + B):-

sin (A + B) = sin A cos B + cosA sin B

sin 2x = sin (x + x) = sin x cos x + cos x sin x

= sin x cos x + sin x cos x

= 2 sin x cos x

Therefore:-

3sin 2x = 3 (2 sin x cos x) which is as required.

Answer 2

Look at the formula for sin 2x, which you surely have been taught.

Answer 3

trigonometric identity: sin(A+B)=sin(A)cos(B)+cos(A)sin(B)
use A=x and B=x in the above identity to get your result.
follow this link to find out how the above identity is derived:
http://www.phy6.org/stargaze/Strig5.htm

Answer 4

trigonometric indentity

sin2x=2sinx cox

just review you notes or book

Answer 5

sin(a+b)= sin(a)cos(b)+sin(b)cos(a)

sin(2x)=sin(x+x)
sin(X+x)= sinx cos x+sinx cosx=2 sinxcosx