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
Hoochie [10]
3 years ago
15

4 Tan A/1-Tan^4=Tan2A + Sin2A​

Mathematics
1 answer:
Eva8 [605]3 years ago
7 0

tan(2<em>A</em>) + sin(2<em>A</em>) = sin(2<em>A</em>)/cos(2<em>A</em>) + sin(2<em>A</em>)

• rewrite tan = sin/cos

… = 1/cos(2<em>A</em>) (sin(2<em>A</em>) + sin(2<em>A</em>) cos(2<em>A</em>))

• expand the functions of 2<em>A</em> using the double angle identities

… = 2/(2 cos²(<em>A</em>) - 1) (sin(<em>A</em>) cos(<em>A</em>) + sin(<em>A</em>) cos(<em>A</em>) (cos²(<em>A</em>) - sin²(<em>A</em>)))

• factor out sin(<em>A</em>) cos(<em>A</em>)

… = 2 sin(<em>A</em>) cos(<em>A</em>)/(2 cos²(<em>A</em>) - 1) (1 + cos²(<em>A</em>) - sin²(<em>A</em>))

• simplify the last factor using the Pythagorean identity, 1 - sin²(<em>A</em>) = cos²(<em>A</em>)

… = 2 sin(<em>A</em>) cos(<em>A</em>)/(2 cos²(<em>A</em>) - 1) (2 cos²(<em>A</em>))

• rearrange terms in the product

… = 2 sin(<em>A</em>) cos(<em>A</em>) (2 cos²(<em>A</em>))/(2 cos²(<em>A</em>) - 1)

• combine the factors of 2 in the numerator to get 4, and divide through the rightmost product by cos²(<em>A</em>)

… = 4 sin(<em>A</em>) cos(<em>A</em>) / (2 - 1/cos²(<em>A</em>))

• rewrite cos = 1/sec, i.e. sec = 1/cos

… = 4 sin(<em>A</em>) cos(<em>A</em>) / (2 - sec²(<em>A</em>))

• divide through again by cos²(<em>A</em>)

… = (4 sin(<em>A</em>)/cos(<em>A</em>)) / (2/cos²(<em>A</em>) - sec²(<em>A</em>)/cos²(<em>A</em>))

• rewrite sin/cos = tan and 1/cos = sec

… = 4 tan(<em>A</em>) / (2 sec²(<em>A</em>) - sec⁴(<em>A</em>))

• factor out sec²(<em>A</em>) in the denominator

… = 4 tan(<em>A</em>) / (sec²(<em>A</em>) (2 - sec²(<em>A</em>)))

• rewrite using the Pythagorean identity, sec²(<em>A</em>) = 1 + tan²(<em>A</em>)

… = 4 tan(<em>A</em>) / ((1 + tan²(<em>A</em>)) (2 - (1 + tan²(<em>A</em>))))

• simplify

… = 4 tan(<em>A</em>) / ((1 + tan²(<em>A</em>)) (1 - tan²(<em>A</em>)))

• condense the denominator as the difference of squares

… = 4 tan(<em>A</em>) / (1 - tan⁴(<em>A</em>))

(Note that some of these steps are optional or can be done simultaneously)

You might be interested in
What are the coordinates of the vertex?
faltersainse [42]
(-2,8) is the answer





5 0
3 years ago
Read 2 more answers
I don’t know how to do this question
noname [10]
Can you post link cause there’s no question
5 0
2 years ago
Who of the following functions is graphed
erastovalidia [21]
The following function would be a or d
5 0
3 years ago
What is the horizontal distance from the origin to the point 2,9
Rina8888 [55]

Answer:

2

Step-by-step explanation:

The x-coordinate of point (2, 9) is 2.

The distance from 0 to 2 on a number line is 2.

Answer: 2

5 0
3 years ago
What is the length of AC¯¯¯¯¯ ?
Harman [31]

Answer:

AC = 12.38 cm

Step-by-step explanation:

When there are 2 pairs given, we can use the sine rule to solve the problem.

By pairs we mean "an angle and side opposite to it"

<em>1 pair is 85.2 degree angle and 13 cm, and another pair is 71.6 degree angle and the side AC (which we want to figure out).</em>

<em />

Sine Rule is given by \frac{SinA}{a}=\frac{SinB}{b}

where,

A and B are the two respective angles and a and b are the two respective sides (of the pairs). Plugging all the info and using algebra, we have:

\frac{Sin85.2}{13}=\frac{Sin71.6}{AC}\\AC*Sin85.2=13*Sin71.6\\AC=\frac{13*Sin71.6}{Sin85.2}\\AC=12.38

Thus, AC = 12.38 cm

5 0
3 years ago
Read 2 more answers
Other questions:
  • Suppose your bank honors a check for which you don't have sufficient funds in your checking account. This action means that you'
    7·1 answer
  • what are the new coordinates for (1,4) when rotated 180 degrees and 90 degrees counterclockwise, and 90 degrees clockwise?
    13·1 answer
  • What's the length of a diagonal angle?
    8·2 answers
  • Four friends ordered a pizza cut into eight slices. The whole pizza was eaten, with each friend eating a different number of sli
    13·2 answers
  • Rectangle A has a length of 12 and width of 8. Rectangle B has a length of 15 and a width of 10.
    6·1 answer
  • I just need the answers for 10b and 10c.<br>Please Help Me.​
    15·2 answers
  • Write an equation of the line that passes through the given point and is perpendicular to the given line. 1 (-6, -4); y = 3x + 1
    7·1 answer
  • Which graph shows the system of equations<br><br><br>{2x+3y=5 4x−5y=−1
    6·1 answer
  • the cylinder shaped containing 3 tennis balls is sold at the local sporting goods store the canister has a radius of 1.35 and he
    11·1 answer
  • You earned $210 over 3 years on an account with a 7% interest rate. What was your initial deposit (principal)?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!