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
A supermarket needs to display 64 boxes of detergent.
Amiraneli [1.4K]
  • All the listed combination of row and boxes are correct and can be chosen from.

From the question, we are asked to find the row arrangement of a stack of boxes. Let us take a look at each one of the aforelisted answers

  • x rows with 16 boxes in each row
  • 8 rows with x boxes in each row
  • 16 rows with x boxes in each row

Since we are told that the total number of boxes to be stacked is 64, then for the first arrangement, we can deduce that the "x" is going to be 4. This is because multiplying 4 by 16 gives 64. For the second row, using the same calculation, we find that "x" is 8. And that of the third gives our "x" to be 4 as well. We can then adjudge that;

  • 4 rows with 16 boxes in each row
  • 8 rows with 8 boxes in each row
  • 16 rows with 8 boxes in each row

Bearing this in mind, we can see that each of the 3 answers fits into the requirements we are asked.

  • At least 3 rows, and at least 4 boxes in each row.

Hence, all of the options are correct.

To learn more about rows and columns, see here brainly.com/question/13196178

5 0
2 years ago
Examine this algebraic expression:
elena-14-01-66 [18.8K]

Answer:

the variables are 4x and y the coefficients are 12 and the constant is 1/2

5 0
3 years ago
Question down below thanks
lara [203]

Answer:

-x + 1 > 3, and 4x + 6 < -2

Step-by-step explanation:

The inequality reads x < -2, so the arrow follows any values that are less than -2. So we need to simplify each inequality in the following options to see which match x < -2.

-4x+3> -5 simplifies to x < 2 so it's wrong

-2x + 4 > -4 simplifies to x < 4 so it's wrong

-x + 1 > 3 simplifies to x < -2, so it's right

2x + 5 < -3 simplifies to x < -4, so it's wrong

4x+ 6 < -2 simplifies to x < -2, so it's right

7 0
3 years ago
Complete the table to show a proportional relationship
vampirchik [111]
60 divided by 4 is 15. so 2*15= 30 // 6*15= 90 // 8*15=120
8 0
3 years ago
Select all complex numbers<br> 5-√9/4<br> 1+√-3<br> 4-3√-16<br> 2-√12➗5<br> 3+2√-9➗7<br> 9√-7/5
harina [27]

Answer:

5-√9/4    4-3√-16    3+2√-9➗7

Step-by-step explanation:


5 0
3 years ago
Other questions:
  • 5 bottles of lemonade 4 water and 3 juice probabilitiy
    12·1 answer
  • John runs a computer software store. Yesterday he counted 121 people who walked by the store, 66 of whom came into the store. Of
    7·1 answer
  • You are researching the penguin population in the Falkland Islands. There are 1000 penguins in the beginning of the first year:
    12·1 answer
  • 10-4=6 what is the correct term for the number4
    8·1 answer
  • What inequality expression is this
    12·1 answer
  • A plane flew 145km/h faster when it was flying with the wind than it would have flown with still air, if it’s speed with the win
    14·1 answer
  • PLEASE CAN SOMEONE HELP I HAVE 5 mins
    11·1 answer
  • sally had 21 marbles her friendgave her some more.she then had 35 marbles. write an expression that shows how many marbles she h
    11·1 answer
  • How is the pattern changing to get from one term to the next?
    7·2 answers
  • A group of adults plus one child attends a movie at a movie theater tickets cost $11 for adults and three dollars for children t
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!