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11Alexandr11 [23.1K]
3 years ago
9

Cos4theta+cos2theta/ cos4theta-cos2theta= _____

Mathematics
1 answer:
vovangra [49]3 years ago
8 0

\bf \textit{Sum to Product Identities} \\\\ cos(\alpha)+cos(\beta)=2cos\left(\cfrac{\alpha+\beta}{2}\right)cos\left(\cfrac{\alpha-\beta}{2}\right) \\\\\\ cos(\alpha)-cos(\beta)=-2sin\left(\cfrac{\alpha+\beta}{2}\right)sin\left(\cfrac{\alpha-\beta}{2}\right) \\\\[-0.35em] \rule{34em}{0.25pt}

\bf \cfrac{cos(4\theta )+cos(2\theta )}{cos(4\theta )-cos(2\theta )}\implies \cfrac{2cos\left( \frac{4\theta +2\theta }{2} \right)cos\left( \frac{4\theta -2\theta }{2} \right)}{-2sin\left( \frac{4\theta +2\theta }{2} \right)sin\left( \frac{4\theta -2\theta }{2} \right)} \implies \cfrac{cos\left( \frac{6\theta }{2} \right)cos\left( \frac{2\theta }{2} \right)}{-sin\left( \frac{6\theta }{2} \right)sin\left( \frac{2\theta }{2} \right)}

\bf \cfrac{cos(3\theta )cos(\theta )}{-sin(3\theta )sin(\theta )}\implies -\cfrac{cos(3\theta )}{sin(3\theta )}\cdot \cfrac{cos(\theta )}{sin(\theta )}\implies -cot(3\theta )cot(\theta )

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A discount book store sells hardcover books for $8 each and paperbacks for $4 each.The number of hardcover books, h, sold one da
vaieri [72.5K]

Jean-Paul's error is that he should have written the second equation as h = 4 p + 2.

<h3 />

<h3>How to solve an equation?</h3>

The hardcover book is $8 each and paperbacks for $4 each.

The number of hardcover books, h, sold one day was 2 more than four times the number of paperback books, p, sold that same day.

Therefore,

h = 4p + 2

Hence,

8h + 4p = 160

Therefore, the right equation are as follows:

h = 4p + 2

8h + 4p = 160

Hence, Jean-Paul should have written the second equation as h = 4 p + 2.

learn more on equation here: brainly.com/question/8465417

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3 0
2 years ago
How do I simplify 5x + -2x + 6x + -x + 3x + 15x. ?
PtichkaEL [24]

hello there

the answer is 26x

Let's simplify step-by-step.

5x−2x+6x−x+3x+15x

=5x+−2x+6x+−x+3x+15x

Combine Like Terms:

=5x+−2x+6x+−x+3x+15x

=(5x+−2x+6x+−x+3x+15x)

=26x

hope this helps

3 0
3 years ago
The surface area of a triangular pyramid is 80 m2. If the pyramid is enlarged by a scale factor of 2, what is the surface area o
astra-53 [7]
160 m^2 is the answer
4 0
3 years ago
Read 2 more answers
Choose the statistical question. * please help now
Oliga [24]

Answer:

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Step-by-step explanation:

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2 years ago
HELP A line passes through two points with coordinates (6,-8) and (-3,7).
FromTheMoon [43]

Answer:

<em>3y+5x=6</em>

Step-by-step explanation:

<u>Equation of the Line</u>

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)

The line passes through the points (6,-8) and (-3,7), thus:

\displaystyle y+8=\frac{7+8}{-3-6}(x-6)

\displaystyle y+8=\frac{15}{-9}(x-6)

Simplifying:

\displaystyle y+8=-\frac{5}{3}(x-6)

Multiplying by 3:

3(y+8)=-5(x-6)

3y+24=-5x+30

Moving all the variables to the left side:

3y + 5x = 30 - 24

3y + 5x = 6

4 0
3 years ago
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