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
torisob [31]
2 years ago
10

If A+B= 45° then prove that: tanA+ tanB+ tanA. tanB​

Mathematics
1 answer:
Iteru [2.4K]2 years ago
8 0

Answer:

See Explanation

Step-by-step explanation:

A+B= 45 \degree \\  \\ assuming  \:  \tan \: on \: both \: sides \\  \\\implies \: \tan( A+B)=  \tan 45 \degree \\  \\  \implies \: \tan( A+B)=  1 \:  \: \\  (  \because \: \tan 45 \degree = 1) \\  \\ \implies \:  \frac{\tan \: A +\tan \: B }{1 - \tan \: A .\tan \: B }  = 1 \\  \\ \implies \: \tan \: A +\tan \: B = 1 - \tan \: A .\tan \: B \\  \\ \purple{ \implies }\:  \orange{ \bold{\tan \: A +\tan \: B  + \tan \: A .\tan \: B= 1 }} \\  \\ thus \: proved

You might be interested in
R (-3,1) and S (-1,3) are points on a circle. If RS is a diameter, find the equation of the circle.​
ELEN [110]

Answer:

\sf (x+2)^2+(y-2)^2=2

Step-by-step explanation:

If RS is the diameter of the circle, then the midpoint of RS will be the center of the circle.

\sf midpoint=\left(\dfrac{x_s-x_r}{2}+x_r,\dfrac{y_s-y_r}{2}+y_r \right)

             \sf =\left(\dfrac{-1-(-3)}{2}+(-3),\dfrac{3-1}{2}+1 \right)

             \sf =(-2, 2)

Equation of a circle:   \sf (x-h)^2+(y-k)^2=r^2

(where (h, k) is the center and r is the radius)

Substituting found center (-2, 2) into the equation of a circle:

\sf \implies (x-(-2))^2+(y-2)^2=r^2

\sf \implies (x+2)^2+(y-2)^2=r^2

To find \sf r^2, simply substitute one of the points into the equation and solve:

\sf \implies (-3+2)^2+(1-2)^2=r^2

\sf \implies 1+1=r^2

\sf \implies r^2=2

Therefore, the equation of the circle is:

\sf (x+2)^2+(y-2)^2=2

4 0
2 years ago
The value of 8 in the number 874,500 is how many times greater than the value of 8 in the number 8,745? 10 100 1,000 10,000
Lady bird [3.3K]
I divided 8745 by 8 and got 1005 so i would say 1000
5 0
2 years ago
Pls help due soon I’ll be giving brainliest :))
Arada [10]

Answer:

im pretty sure first question is 28.6 seconds

and second one is 276 total pounds

Step-by-step explanation:

The first one is 86 divided by 3 = 28.6 seconds

the second one is 23 x 12 = 276 pounds

8 0
2 years ago
Read 2 more answers
Freemont Run Club surveyed a random sample of 303030 of their members about their running habits. Of the members surveyed, 999 s
devlian [24]

Answer:

the answer is 25 according to Khan

Step-by-step explanation:

3 0
2 years ago
A bag contains 50 blue marbles and 66 red marbles. If 88 more red marbles are added to the bag, how many more blue marbles must
vaieri [72.5K]

Answer:

60

Step-by-step explanation:

After adding 88 red marbles, there are 50 blue marbles out of the 204 marbles total.

Let the number of blue marbles to be added be x.

\frac{50+x}{204+x}=\frac{5}{12} \\ \\ 600+12x=1020+5x \\ \\ 420=7x \\ \\ x=60

7 0
11 months ago
Other questions:
  • Mike ate 1 3 of a bag of peanuts at the game, and on the way home he ate 1 3 of what was left. How much of the bag of peanuts di
    8·1 answer
  • Complete the following proof related to the figure below.
    15·2 answers
  • 8(4-x)=7x+2<br> What is x?
    14·2 answers
  • The scale of a map is 4 cm: 15 km. If the distance on the map between two cities is 7 cm, what is the actual distance?
    14·1 answer
  • So this is drag and drop the box on the left will be counted the first box so pls no scams
    10·2 answers
  • Geometry question finding radius and area<br> Thank You!!
    5·1 answer
  • Which expression is equivalent to (4x^3)(2x)^-4
    7·2 answers
  • Justin has $0.90 worth of nickels and dimes. He has a total of 15 nickels and dimes altogether. Determine the number of nickels,
    7·1 answer
  • 14. Find the length of the unknown leg of the right triangle. 12.75 37.25 ?​
    7·1 answer
  • 45n=25<br> Simplify your answer as much as possible.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!