Help I need this before my class ends !!

option 1 drop down are: even-odd identity, quotient identity, Pythagorean identity, double-number identity.option 2 drop down ar

motikmotik

Answer:

The equation is given below as

$\frac{\cos2x}{\cos x}=\cos x-\sin x\tan x$

Step 1:

We will work on the left-hand side, we will have

$\begin{gathered} \cos x-\sin x\tan x \\ \text{recall that,} \\ Quoitent\text{ identity is} \\ \tan x=\frac{\sin x}{\cos x} \end{gathered}$

By substituting the identity above, we will have

$\begin{gathered} \cos x-\sin x\tan x=\cos x-\frac{\sin x.\sin x}{\cos x}=\cos x-\frac{\sin^2x}{\cos x} \\ \end{gathered}$

Here, we will make use of the quotient identity

Step 2:

By writings an expression, we will have

$\begin{gathered} \cos x-\sin x\tan x=\cos x-\frac{\sin x.\sin x}{\cos x} \\ \cos x-\sin x\tan x=\frac{\cos^2x-\sin^2x}{\cos x} \end{gathered}$

Here, we will use the definition of subtraction

$\cos x-\frac{\sin^2x}{\cos x}$

Step 3:

We will apply the double number identity given below

$\begin{gathered} \cos 2\theta=\cos (\theta+\theta)=\cos ^2\theta-\sin ^2\theta \\ \cos 2x=cos(x+x)=\cos ^2x-\sin ^2x \end{gathered}$

By applying this, we will have

$\frac{\cos^2x-\sin^2x}{\cos x}=\frac{\cos2x}{\cos x}$

Here, we will use the double number identity

$\frac{\cos^2x-\sin^2x}{\cos x}$

5 0

1 year ago

A box with a square base and no top is to be made from a square piece of carboard by cutting 7 in. squares from each corner and

mojhsa [17]

Answer:

The size of the cardboard should be $26 in\ by\ 26in$

Step-by-step explanation:

The diagram for this question is shown on the first uploaded image

The volume of the box is $V = 2527 \ in ^3$

The length and the Width of the card is

L = W = Z

From the question we are told that 7 in squares were cut from each corner

So the length and the width of the box would be

L = W = (Z - 7)

And the height would be H = 7 in

Mathematically the volume of the box can be represented as

$V = Length\ of\ bx * Width\ of\ box * Height\ of\ box$

So the Volume would be

$V = (Z-7)(Z-7) * 7$

Substituting values

$(Z-7) ^2 = \frac{2527}{7}$

$(Z-7) ^2 = 361$

$(Z-7) ^2 = 19^2$

=> $Z - 7 = 19$

$Z = 19 + 7$

$Z =26 \ in$

7 0

3 years ago

What is the equivalent fraction for 9/25

Hatshy [7]

Equivalent Fractions for 9/25:
9/25, 18/50, 27/75, 36/100, 45/125, 54/150, 63/175, 72/200, 81/225, 90/250, and so on ...

8 0

3 years ago

Read 2 more answers

What is the slope of this line?

nataly862011 [7]

Answer: $-\frac{8}{5}$

Remember: RISE/RUN (y/x). Lines that are increasing have a positive slope, and lines that are decreasing have a negative slope.

You can find the slope in two ways:

1. Useful if the line is graphed: count the units between 2 points on the line.

Let's use the points (-1, 4) and (4, -4).

(-1, 4) is 8 units higher than (4, -4) and 5 units to the left of (4, -4).

Because the line is decreasing, the slope is negative.

Therefore, the slope is $-\frac{8}{5}$ .

2. Useful if the line is not graphed: find the difference between the y-coordinate values divided by the difference of the x-coordinate values.

Let's use the points (-1, 4) and (4, -4).
$\frac{-4 - 4}{4 - (-1)} = \frac{-8}{5}$

Therefore, the slope is $-\frac{8}{5}$ .

4 0

3 years ago

Read 2 more answers

Linsay is designing a 5-foot-by-8-foot rectangular poster for her art class. She will cover both diagonals of the poster with st

Llana [10]

The answer would be 19

6 0

3 years ago