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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}

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Plot the corresponding points for the inverse of the function represented by this table of values. x -4 0 3 7
NNADVOKAT [17]

Answer:

See explanation

Step-by-step explanation:

Given the function f(x) for which

\begin{array}{ccccc}x&-4&0&3&7\\ \\f(x)&9&5&2&-2\end {array}

If you want to plot the corresponding points for the inverse of the function f(x), change f(x) into y:  

\begin{array}{ccccc}x&-4&0&3&7\\ \\y&9&5&2&-2\end {array}

switch x and y

\begin{array}{ccccc}y&-4&0&3&7\\ \\x&9&5&2&-2\end {array}

and then change y into f^{-1}(x).

You get

\begin{array}{ccccc}x&9&5&2&-2\\ \\f^{-1}(x)&-4&0&3&7\end {array}

Now plot these points on the coordinate plane (see attached diagram).

3 0
3 years ago
Which inequality represents the phrase "paid more than $2.00"?
Nastasia [14]
Is greater than or equal to $.00
6 0
3 years ago
allison is buying packages of sliced meat for the picnic each package has 20 slicrs of mest 5 are turkey if she buys 80 how many
morpeh [17]
If allison buys 80 packs of meat for the picnic and 5 of those slices in each pack are turkey she would end up with 400 slices of turkey.
7 0
3 years ago
The soccer team collected $800 at a car wash fundraiser. They charged $5.00 for small vehicles and $10.00 for longer vehicles. T
Dahasolnce [82]

There are 160 small cars that were washed because u divide

800/ 5= 160. :P

Hope this helps you!!

4 0
3 years ago
7.) Nate has $267 in bills. None of the bills is greater than $10. He has eleven $10 bills. He has seven fewer $5 bills than $1
slavikrds [6]
Just set up 2 equations. 

267 = 10(11) + 5(x) + 1(y) 
x = y - 7 

you can plug the second into the first and get 

267 = 110 + 5(y - 7) + y 
157 = 5y - 35 + y 
6y = 192 
y = 32 
x = 32 - 7 = 25 

thus, 32 $1's and 25 $5's
3 0
3 years ago
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