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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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What is the simplified form of the expression? k3 [k^7/3] -5
iragen [17]
Simplify the following:
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k^(7 + 3)/3 - 5

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k^10/3 - 5

Put each term in k^10/3 - 5 over the common denominator 3: k^10/3 - 5 = k^10/3 - 15/3:
k^10/3 - 15/3

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3 years ago
Question 5 (1 point)
dexar [7]

Answer:

4.5

Step-by-step explanation:

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3 0
3 years ago
4/5x = 3<br> please solve for x
san4es73 [151]

Answer:

x=15/4 or x=3.75

Step-by-step explanation:

4/5*x=3

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0.8*3.75=3

3 0
3 years ago
5 out of 20 students said ice cream was their favorite snack if they were a hundred six graders how many would chose ice cream P
Rufina [12.5K]

Answer:

<u>25 students</u>

Step-by-step explanation:

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To get to 100 students you would times it by 5 and because we times'd the 20 times 5 we need to do the same to the 5 which would result in 25 students. Hope this helped! xx

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