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
Alex17521 [72]
3 years ago
10

3A%20%20%5C%3A%20%20%3D%20%20%5C%3A%20%20%5Cfrac%7B1%7D%7B4%7D%20%283%20%2B%20%20%5Ccos4%20%5Calpha%20%20%29%20" id="TexFormula1" title=" { \cos^{4}\alpha} \: + \sin^{2} \alpha \: \: = \: \frac{1}{4} (3 + \cos4 \alpha ) " alt=" { \cos^{4}\alpha} \: + \sin^{2} \alpha \: \: = \: \frac{1}{4} (3 + \cos4 \alpha ) " align="absmiddle" class="latex-formula">
Prove::​
Mathematics
1 answer:
timurjin [86]3 years ago
3 0

Answer:

Proved

Step-by-step explanation:

cos^4\alpha +sin^4\alpha =\frac{1}{4}(3+cos4\alpha )\\\\

Take the Left Hand Side:

cos^4\alpha +sin^4\alpha\\\\(cos^2\alpha )^2+(sin^2\alpha )^2\\\\(\frac{1+cos2\alpha }{2})^2+(\frac{1-cos2\alpha }{2})^2  \\\\\frac{1+2cos2\alpha +cos^22\alpha }{4}+\frac{1-2cos2\alpha +cos^22\alpha }{4} \\\\

\frac{1+2cos2\alpha +cos^22\alpha +1-2cos2\alpha +cos^22\alpha }{4} \\\\\frac{2+2cos^22\alpha }{4} \\\\\frac{1+cos^22\alpha }{2} \\\\\frac{1}{2}(1+cos^22\alpha )\\\\

\frac{1}{2}(1+\frac{1+cos4\alpha }{2})

\frac{1}{2}(\frac{2+1+cos4\alpha }{2})\\\\\frac{1}{4}(3+cos4\alpha )\\\\

Hence Proved!

The following identities were used are attached in an image

You might be interested in
I need help with this problem 11/16x8/77
Setler79 [48]

Answer:

1/14

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
The mass of a vase is 0.3kilgram. A flower has a mass that is 0.03 times the mass of the vase. What is the mass of the flower?
deff fn [24]
Hello!

0.3 × 0.03 = 0.009

The mass of the flower is 0.009 kilogram.
8 0
3 years ago
Which of the following are identities?
podryga [215]

Answer:

A. III only

Step-by-step explanation:

In mathematics, an identity is one of the characteristics of algebraic expressions.

Given variable a and b in an algebraic expression, an identity is defined as an equality that remains the same no matter the values that we choose for either variable a or b.

Identity in mathematics makes it very easy to solve algebraic expressions. The two sides of an identity in an algebra can easily be exchanged for each other.

In the above question, we are given 3 Options.

I) 3(5 + 2x) = 15 + 6x

II) y = x + 3

III) (x² - y²) = (x + y) (x - y)

Option I) 3(5 + 2x) = 15 + 6x

Is showing distributive property in mathematics.

Distributive property is :

a(b + c) = ab + ac

Option I is not an identity , therefore it is wrong.

Option II) y = x + 3 is just an algebraic expression.

Only Option III is an identity. This is because it follows the rule of

(a² - b²) = (a + b) (a - b)

We can prove and confirm this be solving the algebraic expression

(x + y) (x - y)

We expand the bracket

x² - xy +xy - y²

x² - y²

Therefore, option A is the correct option.

6 0
3 years ago
Read 2 more answers
Divide. What is the remainder?<br><br> 845 ÷ 73<br><br> 42<br> 11<br> 31<br> 22
astra-53 [7]
The remainder to this question is 42
8 0
3 years ago
Read 2 more answers
Question 11 of 11 The 6 students in Mrs. Baker's class were asked how many minutes it takes them to get to school in the morning
Yuki888 [10]

Answer:

Mean=8.8, Median=8

Step-by-step explanation:

How to find the mean:

First, add all the #'s up. 4+9+12+14+7+7=53

Then divide that by the number or numbers. In this case it is 6.

53/6=8.833... So rounded=8.8

Median:

List numbers lowest to highest

4, 7, 7, 9, 12, 14

Go to the middle number.

Since it is between 7 and 9, it is 7+9=16. 16/2=8

8 is the median

8 0
2 years ago
Other questions:
  • Please help me to answer this
    8·1 answer
  • Plzzz Solve these 7 Questions ASAP !!<br> PLZZZZZZZZZZZ IT'S A REQUEST !!!
    9·1 answer
  • Which are the roots of the quadratic function f(b) = b2 – 75? check all that apply. b = 5 square root of 3 b = -5 square root of
    7·1 answer
  • 3. What is the slope of a line with the<br> equation y = 5x+2?
    8·2 answers
  • Help Fast!!!WILL GIVE BRAINLIEST
    14·2 answers
  • Write the expression 2a+b in the form of a fraction with the given denominator. Check if the domain of the expression changed. I
    6·1 answer
  • The amount y (in cups) of flour is proportional to the number x of eggs in a recipe. The recipe calls for 6 cups of flour for ev
    13·1 answer
  • I will give u 5 stars for you answer and ill mark u brainilest if u tell me how to do it.
    7·1 answer
  • Can somebody help me ?
    15·1 answer
  • Don't guess!
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!