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
Michael got a loan for the Playstation 5. His loan was $600. At a 3.75% interest rate he had to pay $7.50 in interest. How long
Semmy [17]

Answer:

4 mo.

Step-by-step explanation:

I = PRT      P = 600    R = .0375    I = 7.50

7.50 = 600(.0375)T

7.5 = 22.5T

T = 7.5/22.5 = 1/3 yr = 4 mo.

6 0
2 years ago
Please solve these questions on the topic of exponents
galina1969 [7]

Answer/Step-by-step explanation:

Recall: x^{-a} = \frac{1}{x^a}

a. 4^{-3} = \frac{1}{4^3} = \frac{1}{64}

b. 13^{-2} = \frac{1}{13^2} = \frac{1}{169}

c. (-3)^{-2} = \frac{1}{-3^2} = \frac{1}{9}

6 0
3 years ago
<img src="https://tex.z-dn.net/?f=2%28%203x%20%2B%201%29%20%3D%2011" id="TexFormula1" title="2( 3x + 1) = 11" alt="2( 3x + 1) =
lisabon 2012 [21]

I'm assuming you need to evaluate/simplify the equation, so you need to isolate/get x by itself in the equation:

2(3x + 1) = 11        Divide by 2 on both sides

3x + 1 = \frac{11}{2}        [11/2 or 5.5] Subtract by 1 on both sides

3x=\frac{11}{2}-\frac{2}{2}            [make the denominator the same to combine fractions]

3x = \frac{9}{2}        Divide by 3 on both sides

x = \frac{9}{6}=\frac{3}{2}  

7 0
3 years ago
I need help ASAP.... please help....
avanturin [10]

Answer:

(7x-1)(x-3)

Step-by-step explanation:

7x^2 - 22x + 3

The factors have to add to -22, but multiply to equal 3. But since the "a" value has a number on it, you have to use it too.

(7x +/- [n1]) ( x +/- [n2]) = 7x^2 - 22x + 3

Since the two numbers multiply to a positive value, they have to have the same sign. (7x-1) (x-3) works to produce the expression when it's foiled.

3 0
3 years ago
Read 2 more answers
Help with this question?? :c
mojhsa [17]
The answer is 1.52 to your question.
5 0
3 years ago
Other questions:
  • Suppose the total cost for n tickets is $36 what's is the total cost of one more ticket is purchased
    15·1 answer
  • Is √25 a real, rational, irrational, integer, whole, or natural number?? Btw it could be more than one!
    5·2 answers
  • Approximately how much money would Manny have if he invested $1,200 at an interest rate
    6·1 answer
  • What advantages does money have over bartered goods? Check all that apply.
    11·2 answers
  • Which number is a solution to x2+8x+12=0?
    14·1 answer
  • Pls help this is due in 2mins
    12·1 answer
  • Make a number line and show all values of x such that: x less than or equal to -2 or x&lt;-5
    9·1 answer
  • Two athletic shoe brands were studied to see which brand was manufactured with the least amount of defects. Brand A was found to
    8·2 answers
  • Calculate the mean for 31 29 33 37 43 38 33 40
    14·2 answers
  • How many cubes with side lengths of 1/2 cm does it take to fill the prism.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!