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
iren [92.7K]
3 years ago
10

Use the identity tan(theta) = sin(theta) / cos(theta) to show that tan(???? + ????) = tan(????)+tan(????) / 1−tan(????) tan(????

)
.
Mathematics
1 answer:
VMariaS [17]3 years ago
8 0

Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof the following indentity:

tan(x+y) = \frac{tan (x) + tan(y)}{1- tan(x) tan(y)}

So we need to begin with the definition of tangent, we know that tan (x) =\frac{sin(x)}{cos(x)} and we can do this:

tan (x+y) = \frac{sin (x+y)}{cos(x+y)}   (1)

We also have the following identities:

sin (a+b) = sin (a) cos(b) + sin (b) cos(a)

cos(a+b)= cos(a) cos(b) - sin(a) sin(b)

Now we can apply those identities into equation (1) like this:

tan (x+y) =\frac{sin (x) cos(y) + sin (y) cos(x)}{cos(x) cos(y) - sin(x) sin(y)}   (2)

We can divide numerator and denominator from expression (2) by \frac{1}{cos(x) cos(y)} we got this:

tan (x+y) = \frac{\frac{sin (x) cos(y)}{cos (x) cos(y)} + \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{cos(x) cos(y)}{cos(x) cos(y)} -\frac{sin(x)sin(y)}{cos(x) cos(y)}}

And simplifying we got:

tan (x+y) = \frac{tan(x) + tan(y)}{1-tan(x) tan(y)}

And that complete the proof.

You might be interested in
Can anyone help me out on this
Licemer1 [7]

Answer:

y=x+10

Step-by-step explanation:

y=mx+b

y=1x+b

1 because for every 10 it goes to the right, it goes up 10 as well.

b=10 because the function crosses the y-axis at 10

so

y=x+10

4 0
3 years ago
I need the side of length x and the answer should be the nearest hundredth
Firdavs [7]

Answer:

x = 15.49

Step-by-step explanation:

a2+b2=c2

11^2+x^2=19^2

121 =x^2 = 361

x^2 = 240

x = 15.49

7 0
2 years ago
What you did to solve this problem?
aev [14]

Answer:

x=8.6

Step-by-step explanation:

0.5x=4.3

/0.5 /0.5

x=8.6

3 0
3 years ago
Mrs. Elizondo runs around a 400-meter track at a constant speed of 250 meter per minute. How many minutes does it take Mrs. Eliz
anastassius [24]

Answer: See explanation

Step-by-step explanation:

From the information, we are told that Mrs. Elizondo runs around a 400-meter track. If she runs 4 laps, the total meters will be:

= 400 × 4

= 1600 meters

Since she uses a constant speed of 250 meter per minute. The number if minutes taken to complete the 4 laps will be gotten by dividing 1600 by 250. This will be:

= 1600 / 250

= 6.4 minutes

= 6 minutes + (0.4 × 60 seconds).

= 6 minutes 24 seconds

3 0
3 years ago
A cable is 30 meters long. How long is the cable in decimeters? Be sure to include the correct unit in your answer.
vekshin1
One metre=10 decimetres.
Therefore 30 metres = 30*10=300 decimetres.
5 0
3 years ago
Other questions:
  • Let y(????)y(t) be a solution of y˙=17y(1−y7)y˙=17y(1−y7) such that y(0)=14y(0)=14. Determine lim????→[infinity]y(????)limt→[inf
    5·1 answer
  • Find the y-intercept of the parabola y= x^2+3/10
    11·2 answers
  • Peter earned $180 working at a store during the summer months. He bought 4 books worth $12 each from his earnings at the store.
    6·2 answers
  • If 20 hens can lay 160 eggs in 16 days, how long would it take 10 hens to lay 40 eggs?
    6·2 answers
  • Find the value of x. (Note: the line passing through the center of the circle is a diameter)
    6·1 answer
  • Please help what is 9999.67 as a fraction
    10·2 answers
  • What is 4,173 in exponential form
    6·1 answer
  • Pls help meeeeeeee with this
    12·1 answer
  • HELP PLSSS!!! NO LINKS!!!
    15·1 answer
  • What is the slope passing through the points (11,-5) and (1,20)
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!