question is:
sin(3x) = 3sinx-4sin³x
there is a clue..
it's that sin(3x)=sin (2x+x)
please help!! and as fast as possible!!
message me or whatever is possible!
question is:
sin(3x) = 3sinx-4sin³x
there is a clue..
it's that sin(3x)=sin (2x+x)
please help!! and as fast as possible!!
message me or whatever is possible!
sin(3x) = 3sinx-4sin³x
there is a clue..
it's that sin(3x)=sin (2x+x)
We can start by rewriting the left side of the equation as per suggestion:
sin(2x+x) = 3sinx-4sin³x
Use the following identity for sine sum formula:
sin(A+B)=sin A cos B + cos A sin B
Again, rewrite the left side of the equation with the formula:
sin2x*cosx + cos2x*sinx = 3sinx - 4sin³x
Use the following double angle formulas:
sin2x = 2sinxcosx
cos2x = (cosx)^2 - (sinx)^2
Rewrite the left side of the equation using these double angle formulas:
2sinxcosx*cosx + ((cosx)^2 - (sinx)^2)*sinx = 3sinx - 4sin³x
Divide both sides by sinx to yield:
2(cosx)^2 + (cosx)^2 - (sinx)^2 = 3 - 4*(sinx)^2
Add like terms:
3*(cosx)^2 = 3 - 3*(sinx)^2
Add sine term to both sides:
3*(cosx)^2 + 3*(sinx)^2 = 3
Divide both sides by 3 and you get the true identity:
(cosx)^2 + (sinx)^2 = 1
I hope this is useful.