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
Anon25 [30]
3 years ago
7

2 tan^2 x-sec x+1 =0​

Mathematics
2 answers:
Nataly [62]3 years ago
3 0

Write it with only cos function:

2 * (sin x /cos x)² - 1/cos x + 1 =0

(remember that cos x ≠0)

2sin²x/cos²x - 1/cos x + 1 = 0 /*cos²x

2sin²x - cos x +cos² x = 0

2(1-cos²x)-cos x+cos²x=0

2-2cos²x-cos x + cos²x=0

-cos²x-cos x+2=0 /*(-1)

cos²x+cos x-2=0

I used only these formulas:

tan x = sin x / cos x

sec x = 1/cos x

sin²x + cos² x = 1 (then cos²x = 1-sin²x).

Okay. We've got easy quadratic equation. Substitute t = cos x, remember that -1≤ t ≤1 and t≠0 is a domain.

t²+t-2=0

∆=1²-4*(-2)*1=1+8=9

√∆=3

t1 = (-1+3)/2 = 1 - it is in domain

t2 = (-1-3)/2 = -2 - it's not in domain.

So we reached only cos x = 1.

The solution of this equation is x = 2πk where k is an integral

shusha [124]3 years ago
3 0

Answer:

x = 0, 360   ( 0 = < x  <= 360).

Step-by-step explanation:

2 tan^2 x-sec x+1 =0​

Substituting  tan^2 x =  sec^2 x - 1:

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

2sec^2 x - 2 - sec x + 1 = 0

2 sec^2 x - sec x - 1 = 0

(2 sec x + 1)(sec x - 1) = 0

sec x = -1/2 ,  sec x = 1

1/cos x = -1/2 , cos x = 1

cos x = -2 ( undefined)= so we ignore this),   cos x = 1.

So x = arcos(1) = 0,  360.

You might be interested in
Matchhhhhh themmmmmmmmmm?
umka21 [38]

Answer:

My answer

Step-by-step explanation:

Matching the two set of variables:

1) Contains two outliers

2) Contains no outliers

3) Contains one outlier

4) Contains three outliers

7 0
3 years ago
What is the correlation coefficient r for the data set?
weeeeeb [17]

Answer:

the answer is -0.95

Step-by-step explanation:

8 0
3 years ago
Find the lowest common denominator of and . A. x3y4 B. x2y3 C. xy4 D. x4y5
Blizzard [7]
Lowest Common Denominator refers to lowes t common multiple. These expressions have two terms 'x' and 'y' and we want to choose the expression that has the highest power such that the other expressions can be multiplied into the common denominator.

For the 'x' term, the highest power is x⁴ and for the 'y' term, the highest power is y⁵

Common denominator of A, B, C, and D: x⁴y⁵




5 0
3 years ago
Laura owes $4759 on a credit card with a 20.9% interest rate compounded monthly. What is the monthly payment she should make in
Juliette [100K]
This can be calculated using the formula:
P = L((r/n)*(1 + r/n)^(n*t))/((1 + r/n)^(n*t) - 1)
Where:
L = 4759
r = 0.209
n = 12
t = 3
So plugging in our data:P = 4759((0.209/12)*(1 + 0.209/12)^(12*3))/((1 + 0.209/12)^(12*3) - 1)
Which will give us the amount of: $179.05 is the monthly repayments.
Other info:
Total interest:$1,686.80
Total cost:$6,445.80
8 0
3 years ago
Read 2 more answers
Find the mean of the following data
Evgesh-ka [11]
Hi, the mean for the numbers is 29, B =D
4 0
3 years ago
Read 2 more answers
Other questions:
  • Select the correct text in the passage.
    5·1 answer
  • Can some one help me with this?????
    13·2 answers
  • The diameter of this compact disc is 11.8cm. The hole in the middle has a area of 1.54cm2. What is the area of the plastic in th
    12·1 answer
  • Each month, Kelsey donates 1/5 of her allowance to her school for supplies. 1/2 of that amount goea to the chorus class. How muc
    10·1 answer
  • How to solve this problem?
    12·1 answer
  • Someone help pls! <br><br><br> 4x+3=5x+21
    9·1 answer
  • Clarence has $90 in a savings account that earns 10% annually. The interest is not
    12·1 answer
  • What is the average rate of change of f(x)=x²+4x+4 from x=1 to x=3?​
    15·1 answer
  • Which expression is equivalent n + n - 0.24n?​
    14·1 answer
  • Korina used 9.3 pints of blue paint and white paint to paint her bedroom walls. 3/5 of this amount is blue paint, and the rest i
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!