Question

Prove that cos 5x= 16 cos^5 (x)- 20 cos^3 x- 2 cosx

Answer 1

Answer:

The identities used are:

• cos (A+B) = cos A cos B - sin A sin B

• cos 2A = 2 cos^2 A - 1

• sin 2A = 2 sin A cos A

• cos 3A = 4 cos^3 A - 3 cos A

• sin 3A = 3 sin A - 4 sin^3 A

• sin^2 A = 1 - cos ^2 A

Hope it helps!

Answer 2

Step-by-step explanation:

Use the short-hands c=cosx, s=sinx and continue with

cos5x+isin5x=(c+is)5=c5−10s2c3+5s4c+i(s5−10s3c2+5sc4)

=c5−10(1−c2)c3+5(1−c2)2c+i(s5−10s3(1−s2)+5s(1−s2)2)

=16c5−20c3+5c+i(16s5−20s3+5s)

where c2+s2=1 is used. Thus,

cos5x=16cos5x−20cos3x+5cosx

sin5x=16sin5x−20sin3x+5sinx