SOLUTION: Verify the given identity. sin 4x = 4 sin x cos3 x − 4 cos x sin3 x Repeatedly use the Double-Angle Identities as needed, and then multiply out the products. (Simplify complete

Algebra ->  Trigonometry-basics -> SOLUTION: Verify the given identity. sin 4x = 4 sin x cos3 x − 4 cos x sin3 x Repeatedly use the Double-Angle Identities as needed, and then multiply out the products. (Simplify complete      Log On


   



Question 1178306: Verify the given identity.
sin 4x = 4 sin x cos3 x − 4 cos x sin3 x
Repeatedly use the Double-Angle Identities as needed, and then multiply out the products. (Simplify completely at each step.)
sin 4x = 2(sin 2x) (cos(2x))
=2(2 sin x)(blank))(cos^2 x − sin(x)^2
=4 sin x cos^3 x − (blank)
I just need help filling in the two blanks. I did 2 of them already but just don't know what the other 2 are.




Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

sin+%284x%29+=+4sin+%28x%29+cos%5E3%28x%29+-+4cos+%28x%29+sin%5E3%28x%29
Repeatedly use the Double-Angle Identities as needed, and then multiply out the products. (Simplify completely at each step.)

sin+%284x%29+=+4sin+%28x%29+cos%5E3%28x%29+-+4cos+%28x%29+sin%5E3%28x%29........cos%5E3%28x%29=%281%2F4%29+%283cos%28x%29+%2B+cos%283+x%29%29 and sin%5E3%28x%29=%281%2F4+%29%283+sin%28x%29+-+sin%283+x%29%29







sin+%284x%29+=++sin+%28x%29cos%283+x%29%29++%2B+cos+%28x%29+sin%283+x%29%29....cos%283+x%29=cos%28x%29+%282+cos%282+x%29+-+1%29, and sin%283+x%29=sin%28x%29+%282+cos%282+x%29+%2B+1%29



sin+%284x%29+=++sin+%28x%29cos%28x%29+%282+cos%282+x%29+-+1%2B+2+cos%282+x%29+%2B+1%29

sin+%284x%29+=++sin+%28x%29cos%28x%29+%284+cos%282x%29+%29....sin+%28x%29cos%28x%29=%281%2F2%29+sin%282+x%29

sin+%284x%29+=++%281%2Fcross%282%29%29+sin%282+x%29+%28cross%284+%292cos%282x%29+%29

sin+%284x%29+=++sin%282x%29%282cos%282x%29%29

sin+%284x%29+=+2sin%282x%29cos%282x%29+

sin+%284x%29+=+sin%284x%29+