Question

HELP ME!!

Drag each tile to the correct box.
Arrange the steps in the correct order to express in terms of .

Answer 1

The arranged steps are shown below.

Explanation:

The given expression is

`\cos 3x`

We need to express the given expression in terms of cos x.

The arranged steps are shown below:

`\cos (2x+x)`

`\cos (2x)\cos (x)-\sin (2x)\sin (x)`

`[1-2\sin^2 (x)]\cos (x)-[2\sin (x)\cos (x)]\sin (x)`
`[\because \cos (2x)=1-2\sin^2 (x),\sin (2x)=2\sin (x)\cos (x)]`

`\cos (x)-2\sin^2 (x)\cos (x)-2\sin^2 (x)\cos (x)`

`\cos (x)-4\sin^2 (x)\cos (x)`

`\cos (x)[1-4\sin^2 (x)]`

`\cos (x)\{1-4[1-\cos^2 (x)]\}`
`[\because \sin^2 (x)=1-\cos^2 (x)]`

`\cos (x)[-3+4\cos^2 (x)]`

`4\cos^3 (x)-3\cos (x)`

Answer 2

arranged

Explanation:

1. cos(2x+x)

2. cos2xcos-sin2xsinx

3. 1-2sin^2x(cosx) -(2sinxcosx)sinx

4. cosx - 2sin^2xcosx - 2sin^2xcosx

5. cosx - 4sin^2xcosx

6. cosx( 1 - 4sin^2x)

7. cosx{1-4(1-cos^2x)}

8. cosx{-3+4cos^2x)

9. 4cos^3x-3cosx !