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
gavmur [86]
3 years ago
12

Please help with this problem.

Mathematics
1 answer:
larisa86 [58]3 years ago
6 0

Answer:

60°, 120°

Step-by-step explanation:

\frac{ {tan}^{2}x }{2}  - 2 {cos}^{2}x = 1 \\   \\  \frac{ {tan}^{2}x  - 4{cos}^{2}x }{2} = 1 \\  \\ {tan}^{2}x  - 4{cos}^{2}x = 2 \\  \\  \frac{{sin}^{2}x}{{cos}^{2}x} - 4{cos}^{2}x = 2 \\  \\ \frac{{sin}^{2}x - 4{cos}^{4}x}{{cos}^{2}x}  = 2 \\  \\ {sin}^{2}x - 4{cos}^{4}x = 2{cos}^{2}x \\  \\ 4{cos}^{4}x  + 2{cos}^{2}x - {sin}^{2}x = 0  \\  \\ 4{cos}^{4}x  + 2{cos}^{2}x  +  {cos}^{2}x  - 1= 0  \\  \\ 4{cos}^{4}x  + 3{cos}^{2}x   - 1= 0  \\  \\ 4{cos}^{4}x  + 4{cos}^{2}x -   {cos}^{2}x - 1= 0  \\  \\4{cos}^{2}x({cos}^{2}x + 1) - 1({cos}^{2}x + 1) = 0 \\  \\ ({cos}^{2}x + 1)(4{cos}^{2}x - 1) = 0 \\  \\ ({cos}^{2}x + 1) = 0 \: or \: (4{cos}^{2}x - 1) = 0 \\  \\ {cos}^{2}x =  - 1 \: or \: 4{cos}^{2}x = 1 \\  \\ {cos}x = \sqrt{ - 1}  \: which \: is \: not \: possible \\  \therefore \: {cos}^{2}x =  \frac{1}{4}  \\  \\ \therefore \: {cos}x =   \pm\frac{1}{2} \\  \\ \therefore \: {cos}x =   \frac{1}{2}  \: or \: {cos}x =    - \frac{1}{2}  \\  \\ \therefore \: {cos}x =   {cos}60 \degree \: or \: {cos}x =     {cos}120 \degree \\  \\ \therefore \:x = 60 \degree \:  \: or  \: \: x  = 120 \degree

You might be interested in
Pls <br> helppp<br><br><br> thanks!!!
True [87]

Answer:

64 inch³

Step-by-step explanation:

3 / 2 = 1.5 radius

1.5²x π x 10 = 22.5 π = volume

22.5 π x 9/10 = 20.25π of water

= 63.6172512352

3 0
2 years ago
Wha it is 2,200 divided by 30 and 2,300 divided by 30
Paladinen [302]

Answer:

2,200/30=73.3333333

2,300/30=76.6666667

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
A building is 50 feet tall. Imagine you are standing 30 feet away from it. What is the angle when you are looking up at your fri
Rina8888 [55]

Answer:

53.1

Step-by-step explanation:

I used my protractor and that is what I got there is no detailed explanation that I came up with

5 0
3 years ago
Garden A has 9 more currant bushes than Garden B. If 3 currant bushes are transplanted from Garden B to Garden A, then Garden A
marusya05 [52]

Answer:

42

Step-by-step explanation:

Let x = the original number of bushes in garden A

Let x-9 = the original number of bushes in garden B

x-9-3=x-12 = bushes in garden B after transplanting 3

x+3 = bushes in garden A after transplanting 3

x+3=1.5(x-12)

x+3=1.5x-18

0.5x=21

x=42

There were 42 current bushes in garden A

3 0
3 years ago
Read 2 more answers
Writing
Afina-wow [57]

Answer:

b=17

Step-by-step explanation:

b=(45+6)/3

b=51/3

b=17

she bought 17 books since the original price of evereything was 51 dollars before the discount of 6 dollars.

3 0
2 years ago
Other questions:
  • If [infinity] cn8n n = 0 is convergent, can we conclude that each of the following series is convergent? (a) [infinity] cn(−3)n
    11·1 answer
  • Jack invests $1500 at a certain annual interest rate, and he invests another $3000 at an annual rate that is one-half percent hi
    13·1 answer
  • My neighbor is buying new carpet for her bedroom floor. The length of the bedroom is 16 feet. The area of the bedroom is 288 squ
    5·1 answer
  • 7x-8(-2x+9)=112 <br> What is x
    11·2 answers
  • Y=mx+b is used for what math equation
    8·2 answers
  • Please Help). Polygon ABCD is the result of translation of polygon EFGH. AB is parallel to DC in the pre-image. Will Mark Brainl
    15·1 answer
  • Please help, we only have about a few minutes left.
    14·1 answer
  • Pl3sssssssssssssssssssssssssssss
    14·1 answer
  • In the art room there are a total of 42 paintbrushes. 30 are large and the rest are small. What is the ratio of small paintbrush
    13·1 answer
  • Solve for xx. Round to the nearest tenth of a degree, if necessary.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!