Question

Rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

cos^3 x

Answer 1

@Libniz

Answer 2

i dont understand step 3 and 4..

Answer 3

cos(x)^3=

since cos(x)^2= 1/2(cos(2x)+1)
1/2(cos(2x)+1) cos(x)

Answer 4

From Mathematica:\[\cos ^3(x)=\frac{1}{4} (3 \cos (x)+\cos (3 x)) \]

Answer 5

A. (3/4) cos x + (1/4) cos 3x + cos 2x

B. (3/4) cos x + (1/4)cos 3x

C.(3/4) cos x - (1/4) cos 3x

D.(3/4) cos x - (1/4) cos 3x - cos 2x

Answer 6

B:\[\frac{3 \text{ Cos}[x]}{4}+\frac{1}{4} \text{Cos}[3 x] \]

Answer 7

@robtobey could u explain why?

Answer 8

\[cos(x)=\frac{1}{2}(e^{it}+e^{-it})\]
\[cos^3(x)=\frac{1}{2}(e^{it}+e^{-it})^3\]
foil
\[\frac{3 e^{-i t}}{8}+\frac{3 e^{i t}}{8}+\frac{1}{8} e^{-3 i t}+\frac{1}{8} e^{3 i t}\]

\[\frac{1}{2}\left(\frac{3 e^{-i t}}{4}+\frac{3 e^{i t}}{4}+\frac{1}{4} e^{-3 i t}+\frac{1}{4} e^{3 i t}\right)\]

so
it is

\[\frac{3}{4} cos[x]+\frac{1}{4} cos[x]\]

Answer 9

ok thank u! @libniz

Answer 10

ok let me do this now