[tex] \binom{ \sin( \alpha) + \sin( 2alpha ) }{1 + \cos( \alpha ) + \cos(2 \alpha ) } = \tan( \alpha ) [/tex]

Answers

Answer 1

I see you use the TeX command "\binom" for binomial coefficient, but I think you meant to use "\frac" to write a fraction, namely,

[tex]\dfrac{\sin(\alpha)+\sin(2\alpha)}{1+\cos(\alpha)+\cos(2\alpha)}=\tan(\alpha)[/tex]

and I assume you're supposed to establish an identity.

Recall the double angle identities for cos and sin :

cos(2α) = cos²(α) - sin²(α) = 2 cos²(α) - 1

sin(2α) = 2 sin(α) cos(α)

Now expand the left side as

(sin(α) + sin(2α)) / (1 + cos(α) + cos(2α)) = (sin(α) + 2 sin(α) cos(α)) / (1 + cos(α) + 2 cos²(α) - 1)

Factor sin(α) from the numerator, and after canceling the 1s in the denominator and factor cos(α) :

… = [sin(α) (1 + 2 cos(α))] / [cos(α) (1 + 2 cos(α))]

Cancel the factors of 1 + 2 cos(α) :

… = sin(α) / cos(α)

which is equivalent to

… = tan(α)

by definition of tan.


Related Questions

“if there are 12 boys and 48 girls in a room, fill out all of the possible ratios of boys to girls that could be made.”

Answers

Answer:

1 boy 4 girls, 2 boys 8 girls, 3 boys 12 girls, 4 boys 16 girls

59.904 simplified. (help) ​

Answers

Answer:

59 113/125  

Step-by-step explanation:

10 points AND BRAINLIEST EASY QUESTION MUST BE DONE IN 10 MIN OR LESS. NO TROLL ANSWERS​

Answers

Answer:

Initial Value=15

Rate of change=15/10=1.5

Equation: y=1.5x+15

Step-by-step explanation:

y=ax+b

y=1.5x+b

15=1.5(0)+b

b=15

The first term of an arithmetic sequence is -5, and the tenth term is 13.

Find the common difference.

2
1.8
8/9

Answers

Answer:

Step-by-step explanation:

Let d be the common difference.

a₁₀ = a₁ + (10-1)d

13 = -5 + 9d

d = 2

help please i beg you

Answers

Answer:

4800

Step-by-step explanation:

Answer:

108

Step-by-step explanation:

if u need step by step explanation please comment

what is 2X500 pls!!!!!

Answers

Answer:

1000

Step-by-step explanation:

2×500=1000

hope it helps

Adam wishes to have ​$21 comma 000

available in 22

years to purchase a new car for his son as a gift for his college

graduation. To accomplish this​ goal, how much should Adam invest now in a CD that pays 1.78
​%
interest compounded semiannually
​? round to the nearest cent as needed

Answers

Answer:

la respuesta que buscas es bastante simple pero no lo sé

Step-by-step explanation:

Write the slope of a line parallel to the given line. y=8x+3

Answers

Answer:

8

Step-by-step explanation:

Slope of parallel lines are equal

In the equation y=8x+3,

8 stands for the slope

-3 > t+5/-1
can someone plz solve this inequality

Answers

simplify:

-3 - (-t - 5) > 0

t + 2 > 0

t > -2

Have an amazing day :)
Will give brainlst! Pls help

Answers

Answer:

C. As the Test Score increases, the Social media time decreases

Step-by-step explanation:

D. Yes, linear because if I were to draw a line on the graph most of the points on the scatter plots would match?

Answer:

C. As the Social media time increases, the Test score decreases.

D. Yes, I think the relationship between the test scores and social media time appears liner, because linear lines tend to be straight, and has a constant rate of change. In this case, there is a constant rate of change, and the plot points aren't all over the place.

Explanation (sort of):

Look at the graph going from left to right; You will see that the plot points continue to "fall" closer to the x-axis. This is why "Test scores" are decreasing instead of "Social media time", unlike what someone else answered with.

find the quotient 1 7/8 / 5 5/8

Answers

this would be 1/3
explanation:
1 7/8= 15/8
5 5/8= 45/8
15/8 / 45/8= .33333 = 1/3

HELPPPPPP math please only correct answer i beg you

Answers

Answer:

the area is 15

Step-by-step explanation:

if you split this shape into a triangle and a square, the triangle would measure with a legnth og 4 and a with of 3, which = 12 and then you divide by 2 to = the triangles area(6) then you add tht to the area of the square 3*3=9. so the answer would be 15

What is the length of side s of the square shown below?
45
8
90°
S
O A. 413
B. 2
O C. 1
D. 6
E. 4
O F. 8-12

Answers

Answer:

A. 4√2..........................

Solve for s. 5s = -5s + 8(2s + 6)
what is s value?​

Answers

Answer:

5s = -5s + 8(2s + 6)

5 s = 11 s + 48

s = -8

so the Solution: S = -8

HOPE THIS HELPS <3 HAVE A NIVE DAYY :)

Which statement about the solution to the system and its justification is true? Please help!!

Answers

Answer:

c i think

Step-by-step explanation:

4/9x6= (write in simplest form)

Answers

Answer:

24/7

Step-by-step explanation:

Answer:

8/3

Step-by-step explanation:

4      *      6      =       24                       8

9                                 9                         3

Which equation is represented by the line

Answers

The correct choice is the third one. Y=2/3x

A raffle is going to be held in which the winner will get $200. If 1000 tickets are to be sold, what is the fair
price for a ticket?

Answers

Answer:

$5

Step-by-step explanation:

1000/200=5

Answer:

20 cents.

Step-by-step explanation:

A fair price would be 200/1000 = 1/5 of a dollar which is 20 cents. But this does not allow for the people putting on the raffle to make any money for doing it. It would be better if the raffle went for a dollar. Most people would think that is fair and would not begrudge a dollar.

Is 2.5 : 8 and 7.5 : 24 equivalent?

Answers

Answer:

Yes

Step-by-step explanation:

[tex]\frac{2.5}{8} = \frac{7.5}{24} = \frac{5}{16}[/tex]

Answer:

yes it is equivalent

because when we multiple 3

to both 2.5 and 8

then it will. 7.5:24

so, answer is yes

hope it helps

100 POINTS IF YOU ANSWER WITH WHHSHSHSS OR SOMTJING GETTING REPORTED AND IT WILL TAKE YOUR POINTS. Math Properties of Equality, Part 2

For each expression, write an equivalent expression to show the

mathematical properties of equality.

Distributive Property:

6(m +4) = ?

Associative Property:

2 + (m + x) = ?

Commutative Property:

x + 3 = ?

Distributive Property:

3(2y - 6) = ?

Distributive Property:

m(y + 5) = ?

Answers

Answer:

Distributive Property:

6m+24

Associative Property:

m+x+2

Distributive Property:

6y-18

Distributive Property:

my+5m

The table shows the width and length of different pictures

Answers

Answer:

There is no table? try taking a screenshot

Step-by-step explanation:

Jada’s babysitter is four times Jada’s current age. In 5 years, Jada will be half her babysitter’s current age.

Answers

Answer:

24

Step-by-step explanation:

We can deduce that Jada's current age from her babysitter's age is 6 years.

Word problems in algebra?

Word problems in algebra involve our ability to discern abstract concepts and define variables that can be used to solve them algebraically. We do so by writing out an equation using variables and solving the equation.

From the given problem;

If Jada's current age = xThen Jada Babysitter = 4x

So,  x + 4x = 1

In five years' time;

Jada Babysitter's age = 5(4x)Jada current age [tex]\mathbf{=\dfrac{5(4x)}{2}}[/tex]

So, we can have the equation:

[tex]\mathbf{\rightarrow \ 5(4x) + \dfrac{5(4x)}{2} = 5}[/tex]

20x + 10x = 5

30x = 5

x = 0.6

Therefore, Jada's current age is [tex]\mathbf{=\dfrac{5(4(0.6))}{2} = 6 years }[/tex]

Learn more about word problems in algebra here:

https://brainly.com/question/21405634

evaluate -3 x +2x-1 if x=-5

Answers

Solution: -3(-5) + 2(-5) -1= 4

Explanation:
Since the value of x is given you have to plug in or substitute it in for x in the equation. The work is shown above.
here is the how to solve this and the final answer

ez math help -thanks

Answers

Answer:

use photo math.....

1) -8

2)9

3)18

3 is 8
4 is 9
5 is 18 hope is helps

What is the measure of the angle at the tail end of the kite?

Answers

Answer:

58°

Step-by-step explanation:

measure of the angle at the tail end of the kite

= 360° - (122° + 90° + 90°)

= 360° - 302°

= 58°

The daily budget of $40, to be spent entirely on coffee and comic books. Each comic book is priced at $8 and each
cup of coffee is priced at $4. To maximize utility, how many cups of coffee and how many comic books should I buy How many total utils will i enjoy?

Answers

Answer:

3 comic books and 4 cups of coffee

Step-by-step explanation:

8 × 3 = 24

4 × 4 = 16

16 + 24 = 40

PLEASE WILL MARK BRAINIEST!!!!!! Jameson and Quincy each deposit $7,000 into accounts that earn 6% interest, but Jameson earns annual simple interest while Quincy earns annual compound interest. Assuming neither one of them makes any deposits or withdrawals for 5 years, which of the following is a true statement?

Jameson will have about $9,367.58 less in his account than Quincy.


Jameson will have about $267.58 less in his account than Quincy.


Jameson will have about $2,367.58 more in his account than Quincy.


Jameson will have about $2,100 more in his account than Quincy.

Answers

Jameson will have about $267.58 less in his account than Quincy.

What is Compound Interest?

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

Here, Jameson deposit Principal = $ 7000

           Duration = 5 years

           Rate of interest = 6 % SI per annum.

For simple Interest,   Amount = P(1+RT)

Total amount in Jameson at the end of 5 years = 7000 ( 1 + 0.06 X 5)

                                                          = 7000 X 1.3

                                                         = $ 9100

Quincy deposit Principal = $ 7000

           Duration = 5 years

           Rate of interest = 6 % CI per annum.

For Compound Interest,   Amount = P(1+R)ⁿ

Total amount in Quincy at the end of 5 years =  7000 ( 1 + 0.06)⁵

                                                                           = 7000 X 1.34

                                                                           = $ 9367.58

Thus, Jameson will have about $267.58 less in his account than Quincy.

Learn more about Compound Interest from:

https://brainly.com/question/14295570

#SPJ1

5. Examine the expression below. Select the answer that correctly completes each statement below. * Enter your answer for all parts below.

Sample Answer: C, B, C

5x+2y+7

a The term 5x could be read as:

A the sum of 5 and x

B. the product of 5 and x

C. the quotient of 5 and x

b. In the expression, 7 is a:

A coefficient

B. constant

C. variable

c. In the expression, 2 is a:

A coefficient

B. constant

C. variable ​

Answers

Answer:

B, B, A.

Step-by-step explanation:

5x means 5 multiplied by x, so is it A, B or C? the product, because that means multiplied. a is B.

For b, we can see that 7 is a constant, because it isn't being multiplied by anything.

For c, 2y is 2 multiplied by y. Y would be the variable, and 2 would be the coefficient.

Quadrilateral ABCD at A(-2,2),B(-2,4),C(2,4), and D(2,2). The quadrilateral is then transformed using the rule(x-2,y+8) to form the image A'B'C'D'. What are the new coordinates of A',B',C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments.

Answers

A(-4,10), B(-4,12), C(0,12), D(0,10). The shape will be exactly the same, just translated.

PLZ Help! Using the chain link rule, how to find f'(5)
given f(x)=(g(x))^3 and

g(5)=-3 and g'(5)=6

Please show steps, I will award 5 stars

Answers

Answer:FOR ALL MY POINTS write an argumentative essay on why dog parks are "helpful or harmful"

READ PROMPT

Step-by-step explanation:

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