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
Sergeu [11.5K]
3 years ago
13

Solve tan 10 - tan 50 +tan 70 with trigonometry.

Mathematics
1 answer:
Jobisdone [24]3 years ago
7 0
Below is the solution, I hope it helps.

  <span>i) tan(70) - tan(50) = tan(60 + 10) - tan(60 - 10) 

= {tan(60) + tan(10)}/{1 - tan(60)*tan(10)} - {tan(60) - tan(10)}/{1 + tan(10)*tan(60)} 

ii) Taking LCM & simplifying with applying tan(60) = √3, the above simplifies to: 

= 8*tan(10)/{1 - 3*tan²(10)} 

iii) So tan(70) - tan(50) + tan(10) = 8*tan(10)/{1 - 3*tan²(10)} + tan(10) 

= [8*tan(10) + tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)} 

= [9*tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)} 

= 3 [3*tan(10) - tan³(10)]/{1 - 3*tan²(10)} 

= 3*tan(30) = 3*(1/√3) = √3 [Proved] 

[Since tan(3A) = {3*tan(A) - tan³(A)}/{1 - 3*tan²(A)}, 
{3*tan(10) - tan³(10)}/{1 - 3*tan²(10)} = tan(3*10) = tan(30)]</span>
You might be interested in
Please help ill give brainliest and follow my insta lol&gt; widowmaker2007
Karo-lina-s [1.5K]
Do u follo back tho lol
7 0
3 years ago
Find the total surface area of the figure below:
kow [346]

Answer:

95

Step-by-step explanation:

Formula -

Triangle Area - 1/2bh

Square - l x w

Triangle - 5 x 7 = 35/2 = 17.5

Since there are four triangle, we will multiply 17.5 x 4 which is equal to 70

Square  - 5 x 5 = 25

Now we add both 70 and 25 which is 95

So the total surface area is 95

8 0
2 years ago
Read 2 more answers
1. 2 4/5v-2/3(4v+1 1/6)
Lerok [7]
1. -48v-5/45     2.44-r/2     3.  x=2
6 0
3 years ago
Read 2 more answers
Write a mathematical sentence that expresses the information given below . Use t as your variable name.Necessary type &lt;= to m
miskamm [114]

Answer:

t + 8° > 82°

Step-by-step explanation:

Given that :

Let t = temperature when Susanne checks at 11:00

If t rises by 8 more degrees, it will break the record high temperature for that day

Record high temperature for the day = 82 degree

Hence,

Temperature at 11:00 + 8° > record high temperature for the day

t + 8° > 82°

6 0
3 years ago
What is the diameter of the circle whose center is at (6,0) and passes through the point (2,-3)
Aleksandr [31]

Answer: 10 units

Step-by-step explanation:

Use the distance formula(√(x1-x2)^2+(y2-y1)^2)

\sqrt{(6-2)^2+(0-(-3))^2} \\\\\sqrt{4^2+3^2}\\\\\sqrt{16+9}\\ \\\sqrt{25}\\ \\5

Thus, the radius of the circle is 5.  Because the diameter is 2r, the diameter = 2(5) = 10

Hope it helps <3

5 0
2 years ago
Read 2 more answers
Other questions:
  • Solve the equation -x=-6<br>X=
    14·2 answers
  • You have 26 cards, each labeled with a letter of the alphabet. What is the probability of drawing a car that is a vowel (excludi
    14·1 answer
  • The cost medium pizza with no toppings is $7.50. The cost of each topping is $0.50. a) what is the equation that represents this
    14·1 answer
  • What is the contrapositive of the following: "If I form a study group then I raise my grades." A. If I work alone then I lower m
    8·1 answer
  • 1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown:
    11·1 answer
  • Drag a vertex of the triangle to change its shape double click or double tap a vertex or side to prevent it from changing
    9·2 answers
  • Someone help me please with this algebra problem
    15·2 answers
  • An uber driver charges a flat fee of $9 to
    12·1 answer
  • A rhombus has sides of length x + 6 inches and a perimeter of 49 inches. Which equation represents this situation?​
    11·2 answers
  • Find what 2/4 is multipled by to to get 2/4 divided by 12. Then solve the problem. Do not reduce your answer.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!