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
Bess [88]
3 years ago
14

Prove that sin^4x + cos^4x= sinxcosx

Mathematics
1 answer:
yKpoI14uk [10]3 years ago
7 0

Answer:

(the relation you wrote is not correct, there may be something missing, so I will simplify the initial expression)

Here we have the equation:

sin^4(x) + cos^4(x)

We can rewrite this as:

(sin^2(x))^2 + (cos^2(x))^2

Now we can add and subtract cos^2(x)*sin^2(x) to get:

(sin^2(x))^2 + (cos^2(x))^2 + 2*cos^2(x)*sin^2(x) - 2*cos^2(x)*sin^2(x)

We can complete squares to get:

(cos^2(x) + sin^2(x))^2 - 2*cos(x)^2*sin(x)^2

and we know that:

cos^2(x) + sin^2(x) = 1

then:

1 - 2*sin(x)^2*cos(x)^2

This is the closest expression to what you wrote.

We also know that:

sin(x)*cos(x) = (1/2)*sin(2*x)

If we replace that, we get:

1 - \frac{sin^2(2*x)}{2}

Then the simplification is:

cos^4(x) + sin^4(x)  = 1 - \frac{sin^2(2*x)}{2}

You might be interested in
A number x plus 10 is more than 2
makvit [3.9K]
X+10>2. The simplified answer is x>-8
4 0
3 years ago
Name the ordered pairs for the vertices on the figure below
Elanso [62]

Answer:

where is the figure?

Step-by-step explanation:

4 0
3 years ago
Please help me with these. <br> Thanks
DIA [1.3K]
5.

f(K) = D^3 => f(25) = 125 => 25 * t = 125 ( because K is directly proportional with D^3 )=> t = 125 / 25 => t = 5 => f(25) = 25 * 5 => K * 5 = D^3 ;

6. 

f(L) = F^3 => f(2) =3^3 =>f(2) = 27 => 2 / t =27 => t = 2 / 27 => t = 0.074 => f(2) = 2 / 0.074 => K / 0.074 = F^3 ;


6 0
3 years ago
Solve this and show work​
just olya [345]

Answer:

1.71

Step-by-step explanation:

x/4 = 3/7

4 * 3 = 12

12/7 = 1.714285714285714

Rounded to the nearest hundreths, the answer is  1.71

6 0
3 years ago
God please help me plz
Nat2105 [25]
You convert 432 sq inches into inches so 20.7846. Then you times that by 6. The answer is 124.7076 and if rounded 124.7
8 0
2 years ago
Other questions:
  • angie has $1,550 in a savings account that pays 2.5% annual simple interest. If she does not make any deposits or withdrawals, h
    13·2 answers
  • What's the exact value of tan(-4pi/3)
    10·1 answer
  • Without evaluating the expression, explain why your answer is positive or negative.
    7·1 answer
  • 90,95,101,98,103,119,124,123,132,127 what is the mean
    11·1 answer
  • Mike discovered that the pool in his backyard is leaking slowly. The pool holds 16,111 gallons of water, and is leaking at a rat
    9·1 answer
  • this is pretty easy to most people its just that ive never studied this (open attachment) im in year 7
    5·2 answers
  • What is mѕТ?<br> ооо<br> 0100°<br> o 108°<br> o 130°<br> 0 160°
    5·1 answer
  • Alex earned $75 mowing lawns. He decided to put $25
    10·1 answer
  • Task: Volume &amp; Surface Area
    12·1 answer
  • After completing a fraction division problem, Clarice used multiplication to check her answer.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!