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
Andrej [43]
3 years ago
6

1 + tanx / 1 + cotx =2

Mathematics
1 answer:
Lera25 [3.4K]3 years ago
4 0

Answer:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or x = tan^(-1)(-(i sqrt(3))/2 + 1/2) + π n_2 for n_2 element Z

Step-by-step explanation:

Solve for x:

1 + cot(x) + tan(x) = 2

Multiply both sides of 1 + cot(x) + tan(x) = 2 by tan(x):

1 + tan(x) + tan^2(x) = 2 tan(x)

Subtract 2 tan(x) from both sides:

1 - tan(x) + tan^2(x) = 0

Subtract 1 from both sides:

tan^2(x) - tan(x) = -1

Add 1/4 to both sides:

1/4 - tan(x) + tan^2(x) = -3/4

Write the left hand side as a square:

(tan(x) - 1/2)^2 = -3/4

Take the square root of both sides:

tan(x) - 1/2 = (i sqrt(3))/2 or tan(x) - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:

tan(x) = 1/2 + (i sqrt(3))/2 or tan(x) - 1/2 = -(i sqrt(3))/2

Take the inverse tangent of both sides:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or tan(x) - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or tan(x) = 1/2 - (i sqrt(3))/2

Take the inverse tangent of both sides:

Answer:  x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or x = tan^(-1)(-(i sqrt(3))/2 + 1/2) + π n_2 for n_2 element Z

You might be interested in
Consider the following equations: f(x) = 2x – 2 and g(x) = 5 - x
zysi [14]

Answer:

The difference in slopes of f(x)\ and\ g(x) is = 3

We can say slope of f(x) is positive  and 3 more than slope of g(x) while slope of g(x)  is negative.

Difference of y-intercepts of f(x)\ and\ g(x) is = -7

We can say the y-intercept of g(x) is positive and 7 units above f(x) while y-intercept of f(x)  is negative.

Step-by-step explanation:

Given equation:

f(x) =2x - 2

g(x) =5-x

We need to find the difference of slopes and y-intercepts of the given equations.

The standard form of a slope intercept equation of line is given by:

y=mx+b

where m represents slope and b represents y-intercept of line.

Writing the given equations in standard form to find slope and y-intercept.

f(x) =2x +(-2)

Slope = 2 and y-intercept =-2

g(x) =(-1)x+5

Slope = -1 and y-intercept =5

The difference in slopes of f(x)\ and\ g(x) is = 2-(-1)=2+1=3

We can say slope of f(x) is positive  and 3 more than slope of g(x) while slope of g(x)  is negative.

Difference of y-intercepts of f(x)\ and\ g(x) is = -2-5=-7

We can say the y-intercept of g(x) is positive and 7 units above f(x) while y-intercept of f(x)  is negative.

5 0
2 years ago
What is the y intercept, and what does it represent?
motikmotik
In the linear equation y = mx + b, y-intercept represents the value of y. It is the point where the line crosses the y-axis(vertical axis)

Finding the y-intercept is done by looking at which point in the graph crosses the y-axis. This point will always have an x-coordinate of zero(0).
4 0
3 years ago
Calculate the mean of: 4.6, 3, 8.1, 9, 12, 3, 9, 3.5, 7, 3.<br> 6.22<br> 5.8<br> 9<br> 3
harkovskaia [24]

Answer:

7.3

Step-by-step explanation:

The mean of 4.6, 3, 8.1, 9, 12, 3, 9, 3.5, 7, 3. 6, 22 , 5.8 , 9 , 3 is 7.3

3 0
2 years ago
Read 2 more answers
Can anyone help me out? thanks
Alik [6]

Answer:

450 cm

Step-by-step explanation:

12 degrees is 1/30 of the circumference because there are 360 degrees in a circle.

The minor arc length of 15 is in the same ratio to the circumference as  the 2 angles , so the circumference = 30 * 15 - 450 cm.

8 0
2 years ago
Read 2 more answers
Which expression results in a rational number?
Elodia [21]

Answer:

4

the fourth expression is a rational

8 0
2 years ago
Read 2 more answers
Other questions:
  • PLEASE ANSWERRRR
    12·1 answer
  • Answer choice D.) is 12/13<br> Please help!!
    5·1 answer
  • Find the number, if 80% of it is 6.4
    13·1 answer
  • Which equation does NOT represent a proportional relationship between two variables with the constant of proportinality of? 1/2
    5·1 answer
  • Anya has a base salary of $200 per week for her part-time sales job. She earns a $10 commission for sales of over $500. This wee
    7·1 answer
  • HELP ME PLEASE I SUCK AT MATH I need work shown on this and I only need 3of Them Done Or Two So I Can Do the last one or soo I T
    14·1 answer
  • All the prizes for the contest were won by Josh. Rewrite in an active voice.
    11·1 answer
  • PLS HELPpslapskodkdosnsplspslpsl
    7·2 answers
  • Jasmine is making cookies for everyone in her class and she wants to make sure everyone gets at least one cookie. The recipe cal
    10·1 answer
  • If we suppose that the volume of Lake Rason is approximately 2.56 x 10^5 km^3 and Lake Rason is 20 times the volume of Lake Rush
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!