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
gayaneshka [121]
3 years ago
10

Prove that tan 10+tan 70'+taniou = tanio tanfo'tam 1oo.​

Mathematics
1 answer:
Galina-37 [17]3 years ago
6 0

Question:

Prove that:

tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)

Answer:

Proved

Step-by-step explanation:

Given

tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)

Required

Prove

tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)

Subtract tan(10) from both sides

- tan(10)+tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100) - tan(10)

tan(70) + tan(100) = tan(10). tan(70). tan(100) - tan(10)

Factorize the right hand size

tan(70) + tan(100) = -tan(10)(-tan(70). tan(100) + 1)

Rewrite as:

tan(70) + tan(100) = -tan(10)(1-tan(70). tan(100))

Divide both sides by 1-tan(70). tan(100)

\frac{tan(70) + tan(100)}{1-tan(70). tan(100)} = \frac{-tan(10)(1-tan(70). tan(100))}{1-tan(70). tan(100))}

\frac{tan(70) + tan(100)}{1-tan(70). tan(100)} = -tan(10)

In trigonometry:

tan(A + B) = \frac{tan(A) + tan(B)}{1 - tan(A)tan(B)}

So:

\frac{tan(70) + tan(100)}{1 - tan(70)tan(100)} can be expressed as: tan(70 + 100)

\frac{tan(70) + tan(100)}{1-tan(70). tan(100)} = -tan(10) gives

tan(70 + 100) = -tan(10)

tan(170) = -tan(10)

In trigonometry:

tan(180 - \theta) = -tan(\theta)

So:

tan(180 - 10) = -tan(10)

Because RHS = LHS

Then:

tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100) has been proven

You might be interested in
Every day, Paula performs physical activity on her treadmill. For an hour, she runs 15,000 meters. Knowing that she spends an ho
natali 33 [55]

Answer: 105 kilometers

Step-by-step explanation:

1 kilometer=1,000 meters

15,000 (meters a day) x 7 (days a week) = 105,000 meters.

Convert the meters to kilometers:

105,000/1,000 = 105 kilometers

3 0
3 years ago
Pre cal/cal master needed
weqwewe [10]
Take x-2 and insert it into 2x^2 + 3x-2 where the x is located 
2x^2 + 3x-2
2(x-2)^2 + 3(x-2)-2

Now work out 2(x-2)^2 + 3(x-2)-2 also follow PEMDAS
2(x-2)^2 + 3(x-2)-2 
Since (x-2)^2 is an Exponent, lets work with that first and expand (x-2)^2.
(x-2)^2
(x -2)(x-2)
x^2 -4x + 4
Now Multiply that by 2 because we have that in 2(x-2)^2
(x-2)^2  =  x^2 -4x + 4
2(x-2)^2  =  2(x^2 -4x + 4)
2(x^2 -4x + 4) = 2x^2 - 8x + 8
2x^2 - 8x + 8

Now that 2(x-2)^2 is done lets move on to 3(x-2).

Use the distributive property and distribute the 3
3(x-2) = 3x - 6

All that is left is the -2 

Now lets put it all together 
2(x-2)^2 + 3(x-2)-2

2x^2 - 8x + 8 + 3x - 6 - 2

Now combine all our like terms 
2x^2 - 8x + 8 + 3x - 6 - 2
Combine:  2x^2      =  2x^2 
Combine: -8x + 3x  =  -5x
Combine:  8 - 6 - 2 =   0

So all we have left is
2x^2 - 5x





5 0
3 years ago
ABDC is a kite . AB =AC and DB=DC , Angle A = 80 degree and angle D=62 degree . find angles B and C​
kotegsom [21]

Step-by-step explanation:

you have quand app download and photo this one and come answer

your questions photo and come answer

4 0
2 years ago
Urgent help neededddd
Wewaii [24]

Answer:

176

Step-by-step explanation:

V=\frac{1}{3}\times 8 \times 6 \times 11=176 \:cm^3

8 0
2 years ago
Can someone help me .
RUDIKE [14]

Answer:

b part is the correct answer

3 0
2 years ago
Other questions:
  • A credit card issuer offers an APR. of 22.08% and compounds interest daily. Which is it most likely to advertise, its APR or it’
    15·2 answers
  • Expand and simplify (2x + 5)^2
    5·2 answers
  • The product of two consecutive even integers is 32 less than the square of the greater integer. Find the smaller integer.
    10·2 answers
  • What is 12 less than 18
    5·2 answers
  • Does anybody know this I need them all answered thank you so much
    6·2 answers
  • The yard behind the Cindy’s house is rectangular in shape and has a perimeter of 72 feet. If the length l of the yard is 18 feet
    8·2 answers
  • The answer to the question in the picture
    12·1 answer
  • A caterer charges a $30 fee plus an additional $6.50 per person. She determines the total cost, C, for x people by using the equ
    14·1 answer
  • Heeellllllppppppppp?? anyonnneeee?<br>​
    9·1 answer
  • A rectangular prism has length of 5 feet and a width of 9 feet. If the surface area of the prism is 174 square feet,
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!