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4 years ago

Trig help ..........

Mathematics

1 answer:

Kaylis [27]4 years ago

3 0

See photo for solution

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<img src="https://tex.z-dn.net/?f=%20%7B%20%5Ccos%5E%7B4%7D%5Calpha%7D%20%5C%3A%20%2B%20%20%20%5Csin%5E%7B2%7D%20%5Calpha%20%5C%

timurjin [86]

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

3 0

3 years ago

Fill in the answer.

OLEGan [10]

Answer:

-9

-2

-10

Step-by-step explanation:

Just follow the equation left to right

4 0

4 years ago

If the simple interest on 6000 for 3 years is 1,620 then what is the insterest rate

fomenos

Answer:

Step-by-step explanation:

Gather information like your principal loan amount, interest rate and total number of months or years that you'll be paying the loan.

Calculate your total interest by using this formula: Principal Loan Amount x Interest Rate x Time (aka Number of Years in Term) = Interest.

3 0

3 years ago

there are 112 males and 78 females working at a hospital. what percentage of hospitals workforce is females?

Juli2301 [7.4K]

<span>112+78=total workforce=190
so 78/190=.410526=41.0526%
</span>

6 0

4 years ago

The sum of three consecutive integers is 345. find the three integers.

Yanka [14]

X - 1 + x + x + 1 = 345
Consecutive means that each member differs by one. Put another way you add one to the previous number to get the next number.

3x = 345
x = 115
x - 1 = 114
x + 1 = 116

5 0

3 years ago

Read 2 more answers