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
Delvig [45]
3 years ago
10

Show that cos2x=cosx

Mathematics
1 answer:
PSYCHO15rus [73]3 years ago
3 0

cos (2x) = cos x

2 cos^2 x -1 = cos x   using the double angle formula

2 cos ^2 x -cos x -1 =0

factor

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

using the zero product property

2 cos x+1 =0    cos x -1 =0

2 cos x = -1       cos x =1

cos x = -1/2       cos x=1

taking the arccos of each side

arccos cos x = arccos (-1/2)         arccos cos x = arccos 1

x = 120 degrees   x=-120   degrees           x=0

remember you get 2 values ( 2nd and 3rd quadrant)

these are the principal values

now we need to add 360

x = 120+ 360n      x=-120+ 360n      x = 0 + 360n  where n is an integer


You might be interested in
Are the equations 9x=5x+4 and 14x=4 equivilant?​
Paha777 [63]

Answer:

No

Step-by-step explanation:

First solve both equations:

1) 9x = 5x + 4

Simplifying

9x = 5x + 4

Reorder the terms:

9x = 4 + 5x

Solving

9x = 4 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

9x + -5x = 4 + 5x + -5x

Combine like terms: 9x + -5x = 4x

4x = 4 + 5x + -5x

Combine like terms: 5x + -5x = 0

4x = 4 + 0

4x = 4

Divide each side by '4'.

x = 1

Simplifying

x = 1

2) 14x = 4

14x = 4 (divide both sides by 14 to get x)

14x/14 = 4/14

x = 0.285714285714

As you can see, the value of x in the second equations is less than one, therefore making these algebraic equations not equivalent.

4 0
2 years ago
Read 2 more answers
Please help!!! I will give brainliest and 50 points<br><br>The question is attached below
Serggg [28]

Answer:

1 + ln 2 - ln x

Step-by-step explanation:

ln ( 2e /x)

We know that ln ( a/b) = ln ( a) - ln (b)

ln (2e) - ln (x)

We also know that ln ( a*b) = ln a  + ln b

ln ( 2) + ln e  - ln x

We know that the ln e = 1

ln 2 + 1 - ln x

Changing the order

1 + ln 2 - ln x

4 0
3 years ago
Here’s for my last question, there is no 0.85 so here is the screenshot ;-;
guapka [62]

Answer:

Step-by-step explanation:

first you multiply 6.5 and 12 to get 78 flowers

then you divide 78 by 68.25 to get the cost of one flower which is $1.14

then you mark me brainliest plz

4 0
3 years ago
Read 2 more answers
Please explain the steps or this equation 3+p=8
ladessa [460]

Answer:

5

Step-by-step explanation:

We can subtract both sides of the equation by 3, getting 3 + p - 3 = 8 - 3.

Then we can evaluate, getting p = 8 - 3 = 5.

3 0
3 years ago
Read 2 more answers
PLEASE HELP ME IT'S DUE TODAY AND IT COULD HELP MY GRADE A LOT
ElenaW [278]

Answer:

c = 13

m∡A = 60°

m∡B = 30°

Step-by-step explanation:

This is a 5-12-13 triangle. However, to make sure, I will put the steps.

Allow for each sides to be denoted as a-b-c, in which c is the hypotenuse (longest side). Set the equation:

a² + b² = c²

Plug in the corresponding numbers to the corresponding variables:

5² + 12² = c²

Simplify. First, solve the exponents, and then add:

(5²) = 5 * 5 = 25

(12²) = 12 * 12 = 144

25 + 144 = c²

c² = 169

Note the equal sign, what you do to one side, you do to the other. Isolate the variable, c, by rooting both sides:

√c² = √169

c = √169 = √(13 * 13) = 13

c = 13

13 is your answer for c.

Note the measurements of the angles. We know that this is a 30-60-90 triangle, and so it will be easy to figure it out. Note that the corresponding angles will depend on that of the opposite side's measurement lengths. The hypotenuse will always be on the opposite side of the largest angle (as given), as c, the longest side, is opposite of ∡C, which is the largest angle (90°). Based on this information, it means that ∡A would be 60° (as it is opposite of the middle number, 12), and ∡B would be 30° (opposite of the smallest number, 5).

8 0
2 years ago
Other questions:
  • John (whose line of sight is 6 ft above horizontal) is trying to estimate the height of a tall oak tree. He first measures the a
    8·1 answer
  • 4 (2/3) is the same as 4 groups of (2/3).
    11·1 answer
  • PLEASE ANSWER ASAP
    8·2 answers
  • 12 565 ft to miles, yards, and feet
    9·2 answers
  • X + y = 10<br> x - y = 2
    13·2 answers
  • Jacob saved 2 thousand dollar bills, 4 hundred dollar bills, and 6 ten dollar bills to buy a car. The car costs 10 times as much
    13·2 answers
  • 54 tacos was sold at lunch. What is six times as many as the number of hotdogs that were sold. How many hotdogs were sold?
    5·1 answer
  • Allen has four times as many cards as Bob, and Jane has twice as many cards as Allen. Together, Allen and Jane have 468 cards. H
    14·2 answers
  • Which has a positive value in Quadrant III?
    8·1 answer
  • 4. In a cricket match a batsman hits of boundary 6 time out of 30 balls find the probability
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!