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
Oxana [17]
2 years ago
12

If A+B+C=

> show that tan A + tan B +tan C = tan A.tan B.tan C
Mathematics
1 answer:
seraphim [82]2 years ago
5 0

Answer:

a + b + c = \pi \\  =  > c=  \pi - a - b \\  <  =  >  \tan(c)  =  \tan(\pi - a - b)  =  -\tan(a + b)

Step-by-step explanation:

we have:

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

we also have:

\tan(a)  \tan(b)  \tan(c)  \\  =  -  \tan(a)  \tan(b)  \tan(a + b)  \\  =  \frac{ -(\tan( a  )   + \tan(b) ) \tan(a)  \tan(b) }{1 -  \tan(a)  \tan(b) }  \\  =  \frac{( \tan(a)  +  \tan(b)) \tan(a)   \tan(b) }{ \tan(a) \tan(b)  - 1 } (2)

from (1)(2) => proven

You might be interested in
Solve the proportion for x
navik [9.2K]

Step-by-step explanation:

72/64=x/8

=> x = (72×8)/64

=> x = 9.

hope this helps you.

5 0
3 years ago
Read 2 more answers
i need help with this if you help me i will mark you as brainliest if its right please dont put the answer in a file
STatiana [176]

Answer:

more than 7

Step-by-step explanation:

4+3 = 7

)sorry if i was wrong(

5 0
2 years ago
Read 2 more answers
To find the area of a triangle, you can use the expression b × h ÷ 2, where b is the base of the triangle and h is its height. W
Stella [2.4K]
This is what u got: 2•8=16/2=8
4 0
2 years ago
Read 2 more answers
A retangle is 12 feet wide and 96 inches long. What is the area of the rectangle
luda_lava [24]

I think the area of the rectangle is 96

8 0
3 years ago
A bag contains 3 red and 5 green sweets
Paladinen [302]

Answer: low

Step-by-step explanation: because  there are more greens than red or might say 20%

3 0
2 years ago
Read 2 more answers
Other questions:
  • Judy lost 15 pounds. Use absolute value to represent the number of pounds Judy lost.
    8·1 answer
  • Tony's Pizza made 52 pizzas today. If each pizza contains 12 slices, estimate how many slices of pizza Tony's Pizza Place made b
    13·2 answers
  • If x-15=7-5(x-4) then x=?<br> 0<br> 5<br> 4<br> 2<br> 7
    11·1 answer
  • Tony rides the bus to and from school. His total riding time each day is 45 minutes. How much time does Tony spend riding to and
    12·2 answers
  • Como se daca el area de un triangulo​
    12·1 answer
  • PLEASE HELP! ITS DUE IN 2 HOURS, I WILL GIVE BRAINLIEST. PLEASE SHOW ON GRAPH
    10·1 answer
  • If you draw just one card for me standard deck what are the chances you will draw a non-prime number
    9·1 answer
  • Can someone solve a - 3 over 7 s = -8<br><br><br> and a + 24 = -15<br><br> STEP BY STEP PLEASE.
    13·2 answers
  • Evaluate 3x2 - 4 when χ= 2.<br> Α. 2<br> Ο Ο Ο<br> Ο Β. 8<br> C. 12<br> Ο D. 32
    12·1 answer
  • A farmer planted 32 rows of sweet peppers. Each row had 16 sweet pepper plants. How many plants does he have ALTOGETHER​
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!