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
Serggg [28]
2 years ago
9

How do you simplify sin^4-cos^4=2sin^2-1?

Mathematics
1 answer:
Naily [24]2 years ago
8 0

\bf \textit{Double Angle Identities} \\\\ cos(2\theta)= \begin{cases} cos^2(\theta)-sin^2(\theta)\\ 1-2sin^2(\theta)\\ 2cos^2(\theta)-1 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}

\bf \begin{array}{llll} sin^4(\theta )-cos^4(\theta )&=&2sin^2(\theta )-1\\[1em] [sin(\theta )]^4-[cos(\theta )]^4&=&-[1-2sin^2(\theta )]\\[1em] \stackrel{\textit{difference of squares}}{[[sin(\theta )]^2]^2-[[cos(\theta )]^2]^2}&=&-[cos^2(\theta )-sin^2(\theta )]\\[1em] [sin^2(\theta )-cos^2(\theta )][sin^2(\theta )+cos^2(\theta )]&=&sin^2(\theta )-cos^2(\theta )\\[1em] [sin^2(\theta )-cos^2(\theta )][1]&=\\\\ sin^2(\theta )-cos^2(\theta ) &=\end{array}

You might be interested in
PLEASE HELP
irina [24]
Take the longer leg length as x

(x-8)^2+x^2=(x+8)^2 \\ \\ x^2-16x+64+x^2=x^2+16x+64 \\ \\ x^2-32x=0

Use the formular
x={ \frac{-b+ \sqrt{ b^2-4ac}}{2a} } \\ \\ x={ \frac{32+32}{2} } \\ \\ x=32

∴ shorter leg = 32 - 8 = 24ft
longer leg = 32ft
hypotenuse = 32 + 8 = 40ft
8 0
3 years ago
Can someone please tell me the answer to this?
Neko [114]
A) 3b-7b
-4b

b) a+a-5a
-3a

c) -3-3r
cannot be simplified, no like terms

d) 7t-8t-8
-t-8

e) -15p-20
cannot be simplified, no like terms

f) -g-g-g
-3g
5 0
3 years ago
HELP ASAP!<br><br> it's for a math quiz so thanks
satela [25.4K]
I’m 90% sure that the answer is 36x
5 0
2 years ago
Which expression is a perfect cube
mamaluj [8]

Answer: some perfect cubes are

8 (2^3)

27 (3^3)

64 (4^3)

there are many perfect cubes

maybe there is more to this question?

Step-by-step explanation:

A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times. If x is a perfect cube of y, then x = y3. Therefore, if we take the cube root of a perfect cube, we get a natural number and not a fraction. Hence, 3√x = y. For example, 8 is a perfect cube because 3√8 = 2.

6 0
2 years ago
Number is: 4,563 Classify the number as natural, whole, integer, rational, or irrational. Select all the sets that are correct. 
svetlana [45]
Natural, whole, integer, rational
6 0
3 years ago
Read 2 more answers
Other questions:
  • Values for relation g are given in the table. Which ordered pair would be found in the inverse of g?
    15·2 answers
  • If you flipped the graph of y = x2 + 2x - 2 vertically, you would get the graph of y = -(x2 + 2x - 2). true or false
    5·2 answers
  • An item on sale costs 25% of the original price. If the original price was $40 , what is the sale price?
    9·2 answers
  • mikisha traveled from tampa to Miami a distance of 280 miles on one tank of gas if her tank holds about 13 gallons of fas ehat w
    10·2 answers
  • 35 rounded to the nearest hundred
    7·2 answers
  • Which strategy for addressing counterclaims should Christopher use to
    10·1 answer
  • Forahigh-riskdriver,thetimeindaysbetweenthe beginning of a year and an accident has an exponential pdf. Suppose an insurance com
    8·1 answer
  • PLEASE HELP ASAP WILL GIVE YOU BRAINLIEST
    15·1 answer
  • Total revenue is 3,000 cost of goods 1,500 total selling expence is 500 what is profit
    10·2 answers
  • Select the correct answer.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!