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
serg [7]
2 years ago
14

If 2tanA=3tanB,then prove that tan(A-B)=sin2B/(5-cos2B) ...?

Mathematics
1 answer:
andreev551 [17]2 years ago
8 0
Tan ( A - B ) = ( tan A - tan B ) / ( 1 + tan A tan B )
tan A = 3 tan B/2
tan ( A - B ) = ((3 tan B/ 2)-tan B) / ( 1 + 3 tan² B/2)=
= (tan B/2)  / ( 2 + 3 sin²B/cos²B )=
= (sin B / cos B) / (( 2cos² B+3sin²B)/cos²B)=
=( sin B cos B ) / ( 2 cos²B + 3 ( 1 - cos² B ) ) =
= (sin B cos B ) / ( 2 cos² B + 3 - 3 cos² B ) =
= ( sin 2 B ) / 2 ( 3 - cos² B ) =
= ( sin 2 B ) / ( 6 - cos² B )=
= ( sin 2 B ) / ( 5 + 1 - 2 cos² B )=
= ( sin 2 B ) / ( 5 + sin² B + cos ² B - 2 cos² B ) =
= ( sin 2 B ) / ( 5 - ( cos² B - sin² B ) ) =
= ( sin 2 B ) / ( 5 - cos 2 B )  - correct 
You might be interested in
Which transformation is happening in the image below​
s2008m [1.1K]

Answer:

B.) Reflection over y=-3

Step-by-step explanation:

8 0
3 years ago
ANSWER QUICKLY!!!!!
Paul [167]

Answer:

1. The possible roots are ±1, ±2, ±3, ±6. These are the factors of the trailing constant (6) divided by the factors of the leading coefficient (1). When the leading coefficient is 1, the possible roots are the factors of the constant

2. The polynomial is easier to evaluate when it is written in Horner form:

 f(x) = ((x -4)x +1)x +6

To show that 2 is a zero, we want to find f(2):

 f(2) = ((2 -4)2 +1)2 +6 = (-4 +1)2 +6 = -6 +6 = 0

 f(2) = 0, so 2 is one of the zeros of this function

3.  Using synthetic division (attached) or polynomial long division, we can divide the given polynomial by (x-2) to find the remaining factors. This division gives (x^2 -2x -3), which can be factored as (x -3)(x +1), so the three actual roots are ...

 x = 2 (from above), x = 3, x = -1 (from our factorization)

4. In factored form, the polynomial can be written ...

 f(x) = (x +1)(x -2)(x -3)

The first factor was found from the fact that 2 was given as a zero of the function. For any zero "a", a factor of the polynomial is (x-a).

The remaining factors were found by factoring the quadratic trinomial that resulted from the division of f(x) by x-2. That trinomial is x^2 -2x -3.

There are a number of methods that can be used to factor x^2 -2x -3. Again, the rational root theorem can help. It suggests that ±1 and ±3 are possible roots.

4 0
2 years ago
explain how you would find how many 1 1/2 cup servings there are in a pot that contains 22 1/2 cups of soup.
11Alexandr11 [23.1K]

Step-by-step explanation:

multiply the 1 1/2 by 2 to get 3.

find the closest number that is divisible by 3

3*7 is 21.

We now have to multiply 7 by 2 since we did that to our mixed number to get a whole number.

There is still a 1 1/2 left over. Simply add 1 to 14.

3 0
2 years ago
Read 2 more answers
A full glass of water can hold á of a bottle.
ikadub [295]

Answer:

2

Step-by-step explanation:

lol

7 0
2 years ago
Which of the following relations is a function?
Dmitrij [34]

Answer: D

Step-by-step explanation:

5 0
2 years ago
Other questions:
  • Theirs a picture on top.. :) <br><br> 15. simplify<br> 16. simplify
    15·1 answer
  • Factor completely, the expression: 2x^3-2x^2-12x
    6·1 answer
  • You roll a regular six-sided cube
    5·1 answer
  • Box and whisker box plot
    6·2 answers
  • Find the perimeter of the rectangle
    5·1 answer
  • What's the factors for 375,66,33
    13·1 answer
  • 8 gallons of soil are needed to fill 6 large plant pots. How many gollons are needed to fill 8 pots? Give your answer as a mixed
    14·1 answer
  • What happened as a result of the fall of the Western Roman Empire?
    6·1 answer
  • 27(n+4)+18n=7(n-18)-40n So confused can yall help me?
    12·2 answers
  • Henry wants to center a towel rack on a wall that is 76.8 inches long. How much space will be between the end of the wall and th
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!