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
forsale [732]
3 years ago
7

Find all solutions in the region [0,2pi) for the equation cos^2(2x)-sin^2(2x)=0

Mathematics
1 answer:
Lynna [10]3 years ago
4 0
\cos^{2}(2x)-\sin^{2}(2x)=0
\rightarrow \sin^{2}(2x)=\cos^{2}(2x)
\rightarrow \frac{\sin^{2}(2x)}{\cos^{2}(2x)}=1
\rightarrow \tan^{2}(2x)=1
\rightarrow \tan(2x)=\pm 1

2x can range anywhere in [0, 4\pi)
So:
\rightarrow 2x=\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}, \frac{9\pi}{4}, \frac{11\pi}{4}, \frac{13\pi}{4}, \frac{15\pi}{4}
\rightarrow x=\frac{\pi}{8}, \frac{3\pi}{8}, \frac{5\pi}{8}, \frac{7\pi}{8}, \frac{9\pi}{8}, \frac{11\pi}{8}, \frac{13\pi}{8}, \frac{15\pi}{8}
You might be interested in
Please help!!!<br> picture below
iVinArrow [24]

Answer:

4^3x=4^(4x+4)

Step-by-step explanation:

You can eliminate the first 2 options since those don’t make sense already, and the last option changed 64 to 2^6 which is correct, but when they changed the other side. They should have multiplied 8 to both x and 1 which would have made the whole term 2^(8x+8) and not 2^(8x+1). Left with the third option, 4 to the power of 3 is 64 so the left side makes sense, 4^3x=64^x, on the right side, 4^4 equals 256, so the whole exponent should multiply by 4 so from 256^(x+1) you get 4^4(x+1) giving 4^(4x+4) making the third choice the right answer.

6 0
2 years ago
You mix 3 and one half quarts of juice with 5 and one fourth quarts of ginger ale to make fruit punch. What is the ratio of the
Romashka [77]

Answer:

1.5:2.25 because there is 1.5 quarts of juice and 2.25 quarts of ginger ale and the you put that with the to sign and there you have it




3 0
3 years ago
Can someone plz help me with this one problem plzzzzz!!
irga5000 [103]

Answer:

B

Step-by-step explanation:

add all of last year's and then divide by 3 witch is 3.1

add all of this year's and then divide by 3 witch is 4.1

now subtract witch will give you 1.0

3 0
2 years ago
Read 2 more answers
PLEASE HELP ME PLEASE ​
Yanka [14]

write the balance of the bank statement in his checkbook

hope this helps :)

7 0
3 years ago
Read 2 more answers
When a number x is added to it's square, the total is 12. find two possible values of x<br>​
Fudgin [204]

Answer:

<h2><u><em>x=3 or x=−4</em></u></h2>

Step-by-step explanation:

when a number x is added to it's square, the total is 12. find two possible values of x

x+x^2=12

x^2+x=12

x^2+x−12=12−12

x^2+x−12=0

(x−3)(x+4)=0

x−3=0 or x+4=0

x=3 or x=−4

x=3 or x=−4

3 0
2 years ago
Other questions:
  • How do I find the area ?
    15·1 answer
  • What is square root of 12 in simplified radical form?
    15·2 answers
  • Could someone show me the steps to this problem
    14·1 answer
  • Help plz.I willl give Brainlist if U are correct and even if u are not
    7·2 answers
  • Which of the following are roots of the polynomial function? Check all that apply.
    15·1 answer
  • Solve the equation <br>r ÷ (-8) =5​
    6·2 answers
  • Juan and sara each measure the length of their 9.6 inch long math book three times they record their measurements as shown below
    7·1 answer
  • 2.
    8·1 answer
  • Need Help ASAP
    13·1 answer
  • Find the area in square units ​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!