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
cluponka [151]
3 years ago
15

Simplify tan9x-tan5x / 1+tan9xtan5x (SHOW WORK)

Mathematics
1 answer:
Charra [1.4K]3 years ago
4 0

Answer:

The simplest form is tan(4x)

Step-by-step explanation:

* Lets revise the identity of the compound angles

- tan(a+b)=\frac{tan(a)+tan(b)}{1-tan(a)tan(b)}

- tan(a-b)=\frac{tan(a)-tan(b)}{1+tan(a)tan(b)}

* Lets solve the problem

- Let 9x = 5x + 4x

∴ tan(9x) = tan(5x + 4x)

- Use the rule of the compound angle

∵ \frac{tan(9x)-tan(5x)}{1+tan(9x)tan(5x)} ⇒ (1)

∵ tan(5x+4x)=\frac{tan(5x)+tan(4x)}{1-tan(5x)tan(4x)} ⇒ (2)

∵ tan(9x) = equation (2)

- Substitute (2) in (1)

∴ \frac{\frac{tan(5x)+tan(4x)}{1-tan(5x)tan(4x)}-tan(5x)}{1+(\frac{tan(5x)+tan(4x)}{1-tan(5x)tan(4x)})tan(5x)}

- Multiply up and down by (1 - tan(5x)tan(4x))

∴ \frac{tan(5x)+tan(4x)-tan(5x)[1-tan(5x)tan(4x)]}{1-tan(5x)tan(4x)+tan(5x)[tan(5x)+tan(4x)]}

- Simplify up and down

∴ \frac{tan(5x)+tan(4x)-tan(5x)+tan^{2}(5x)tan(4x)}{1-tan(5x)tan(4x)+tan^{2}(5x)+tan(5x)tan(4x) }

∴ \frac{tan(4x)+tan^{2}(5x)tan(4x)}{[1+tan^{2}(5x)]}

- Take tan(4x) as a common factor up

∴ \frac{tan(4x)[1+tan^{2}(5x)]}{[1+tan^{2}(5x)]}

- Cancel [1 + tan²(5x)] up and down

∴ The answer is tan(4x)

You might be interested in
PLEASE HELP I WILL GIVE BRAINLIEST!! What is the area of the figure? Enter your answer in the box. in² A square with a length of
m_a_m_a [10]

Answer:

Step-by-step explanation:

10 by 2

7 0
3 years ago
Is parallelogram ABCD a rectangle?
Fantom [35]

Answer:

No

Step-by-step explanation:

Sides AB to DC aren't congruent/parallel

Sides BC to AD aren't congruent/parallel

6 0
3 years ago
27 PTS + BRAINLIEST. I need all of these questions answered. I will award brainliest to the fastest and most correct answer. I w
erik [133]
2 Simpify:
a -4 X x = -4x
b -10 X y = -10y
c -1 X a = -a
d b X (-1) = -b
e -4 X 2m = -8m
f 6 X -3a = -18a
g -8 X -3a = 24a
h -6m X 4 = -24m
i -7 X 8n = -56n
j -a X -3 = 3a
k 6x / -2 = -3x
l -10m / -5 = 2m
m -24a / 8 = -3a
n 2(m+3)-8=2(m)+2(3)-8=2m+6-8=2m-2
o 5(m-1)+9=5(m)+5(-1)+9=5m-5+9=5m+4
p 3(a-5)+10=3(a)+3(-5)+10=3a-15+10=3a-5
q 4(2x+1)-8x=4(2x)+4(1)-8x=8x+4-8x=4
r 3(10-2x)+3x=3(10)+3(-2x)+3x=30-6x+3x=30-3x
s 4(3-x)+9x=4(3)+4(-x)+9x=12-4x+9x=12+5x

3 Simplify by collecting like terms:
a 7a-5b+2a-6b=(7+2)a+(-5-6)b=(9)a+(-11)b=9a-11b
b 11x-2y-5x+7y=(11-5)x+(-2+7)y=(6)x+(5)y=6x+5y
c 3m+2g-5g-4m=(3-4)m+(2-5)g=(-1)m+(-3)g=-m-3g
d 6a-7-9a+10=(6-9)a+(-7+10)=(-3)a+(3)=-3a+3
e 7p-2q-6p+3q=(7-6)p+(-2+3)q=(1)p+(1)q=p+q
f 3x+7-12-5x=(3-5)x+(7-12)=(-2)x+(-5)=-2x-5
g 2ab+3bc-5ab+bc=(2-5)ab+(3+1)bc=(-3)ab+(4)bc=-3ab+4bc
h 6t^2+3t-5t^2-8t=(6-5)t^2+(3-8)t=(1)t^2+(-5)t=t^2-5t
i 9y-6z-9y+5z=(9-9)y+(-6+5)z=(0)y+(-1)z=0-z=-z
j 2k-3k^2-4k+k^2=(2-4)k+(-3+1)k^2=(-2)k+(-2)k^2=-2k-2k^2
k 10t+5w+t-7w=(10+1)t+(5-7)w=(11)t+(-2)w=11t-2w
l 7a-3b-8a-5b=(7-8)a+(-3-5)b=(-1)a+(-8)b=-a-8b
8 0
3 years ago
32
Naddik [55]

Answer:

A

Step-by-step explanation:

Samantha already took up an appointment time slot, and the two people can't be at the appointment at the same time, so it should be A.

7 0
3 years ago
5 over 2w equals 45 over 36
adelina 88 [10]
5/2w=45/36 w=1 over 2 or 1/2
8 0
3 years ago
Other questions:
  • I NEED HELP WITH THIS!! PLEASE HELP ME I NEED IT ASAP<br> 12 POINTS
    11·1 answer
  • Given circle O, angle A has a measure of 36° and the radius is 10 cm, find the area of sector BOC.
    14·1 answer
  • What is the value of x?<br> Enter your answer in the box
    9·1 answer
  • Yasmin has a quarter and a nickel. She flipped both coins. What are the chances that both coins land on heads?
    9·2 answers
  • Solve for w.
    8·1 answer
  • 40,000 is 10 times as much as
    12·2 answers
  • Simplest form for 10 sec 1 min
    9·1 answer
  • What is the account balance?
    12·2 answers
  • Mrs. Spina bought 4 boxes of 8 pork chops. She set aside 12 and separated the rest into packs of4 to freeze. How many packs of c
    13·1 answer
  • I need 5-8 done Complete the statements and explain why
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!