How can you prove that
sin4x= 4 cos x sin x - 8 cos x sin(third power)x

If you have some knowledge of complex numbers: This follows pretty much immediately from Euler's formula and DeMoivre's theorem,

(Euler)

(DeMoivre)

so that is the imaginary part of the expanded left hand side.

If that's unfamiliar to you, you can make use of several identities to expand :

(double angle sine)

(double angle sine and cosine)

(Pythagorean)

15

step-by-step explanation:

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent