1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Inga [223]
2 years ago
12

Please someone help me to prove this. ​

Mathematics
1 answer:
morpeh [17]2 years ago
6 0

Answer:  see proof below

<u>Step-by-step explanation:</u>

Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ

Use the Sum/Difference Identities:

sin(α + β) = sinα · cosβ + cosα · sinβ

cos(α - β) = cosα · cosβ + sinα · sinβ

Use the Unit circle to evaluate: sin45 = cos45 = √2/2

Use the Double Angle Identities:   sin2Ф = 2sinФ · cosФ

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

<u />

<u>Proof LHS → RHS</u>

LHS:                                  2sin(45 + 2A) · cos(45 - 2A)

Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)

Unit Circle:    2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]  

Expand:        2[(1/2)cos²2A  + cos2A·sin2A + (1/2)sin²2A]

Distribute:              cos²2A   + 2cos2A·sin2A + sin²2A  

Pythagorean Identity:    1 + 2cos2A·sin2A

Double Angle:                1 + sin4A

LHS = RHS:  1 + sin4A = 1 + sin4A   \checkmark

You might be interested in
Shakeela is planning to buy a pair of pants that have an original price of $51. The pants are on sale for 50% off and the sales
Mila [183]

Answer:

C) $25 + $1.25

Step-by-step explanation:

1.  51 x .5 = 25.5

2.  25.5 x .05 = 1.275

25 + 1.25  ≈  25.5 + 1.28

6 0
3 years ago
2. Which variable will eliminate? *<br> 3x +6y=27<br> -3x+8y= 1
Anarel [89]
9x=27
x=3
———
-3*3+8y=1
5\4
5 0
3 years ago
Read 2 more answers
A wooden box has the shape of a rectangular prism. The inside of the box is also a rectangular prism. What is the volume of the
ElenaW [278]
1560 cm^2 as you subtract the small prism from the large
5 0
2 years ago
Explain your answer !! <br> Have a nice day <br><br> Will give braisnlt
lora16 [44]

Answer:

The equations are:

4H + 3P = 13.75

2H + 5P = 11.25

Hotdog = 2.50

Pretzel = 1.25

Step-by-step explanation:

Let:

H = hot\ dog

P =Pretzel

For Tina:

4H + 3P = 13.75

For Doug:

2H + 5P = 11.25

Solving for the price of both items:

We have:

4H + 3P = 13.75 --- (1)

2H + 5P = 11.25 --- (2)

Multiply (2) by 2

2 * (2H + 5P = 11.25)

-------------------

4H + 10P = 22.50 --- (3)

Subtract (3) from (1)

4H + 3P = 13.75

4H + 10P = 22.50

----------------------

4H - 4H + 3P - 10P = 13.75 - 22.50

3P - 10P = 13.75 - 22.50

-7P = -8.75

Solve for P

P = \frac{-8.75}{-7}

P = 1.25

Substitute 1.25 for P in (2)

2H + 5P = 11.25

2H + 5 * 1.25 = 11.25

2H + 6.25 = 11.25

Collect Like Terms

2H = 11.25-6.25

2H = 5

Solve for H

H = \frac{5}{2}

H = 2.50

3 0
3 years ago
Pick correct graph from multiple choice options. A. C. B. D.
irina1246 [14]

Answer:

Step-by-step explanation:

x = 2 is the equation of a vertical line passing through x = 2.  This is shown in the lower left graph:  a solid vertical line 2 units to the right of the y-axis.

7 0
3 years ago
Read 2 more answers
Other questions:
  • (25ab^3)^1/3 divided by (ab)^-1/2
    10·1 answer
  • The cost c ( x ) c(x), where x x is the number of miles driven, of renting a car for a day is $49 plus $0.55 per mile.
    13·1 answer
  • In order to convert a temperature in Kelvin, K, into a temperature in degrees Fahrenheit, F, the equation above can be used. Whi
    9·2 answers
  • Which equation can be used to find the number of fish in the pond on June 1?
    5·1 answer
  • If f(x)=x^2-1 what is the equation for f^-1(x)
    9·1 answer
  • about 1300 organ specimens are preserved in fluid. Typically contains 7/10 alcohol and 3/10 water. if one jar contains 19 pins o
    7·1 answer
  • PLEASE HELP BEST ANSWER GETS BRANLIEST
    13·2 answers
  • An equation that models the perimeter of the rectangle 2w+4w=36
    13·1 answer
  • A total of 19,035 people skied at the resort during the 5 days
    13·2 answers
  • What number line shows the solution set to this inequality? -2x + 9 &lt; x − 9
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!