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Hoochie [10]
3 years ago
15

4 Tan A/1-Tan^4=Tan2A + Sin2A​

Mathematics
1 answer:
Eva8 [605]3 years ago
7 0

tan(2<em>A</em>) + sin(2<em>A</em>) = sin(2<em>A</em>)/cos(2<em>A</em>) + sin(2<em>A</em>)

• rewrite tan = sin/cos

… = 1/cos(2<em>A</em>) (sin(2<em>A</em>) + sin(2<em>A</em>) cos(2<em>A</em>))

• expand the functions of 2<em>A</em> using the double angle identities

… = 2/(2 cos²(<em>A</em>) - 1) (sin(<em>A</em>) cos(<em>A</em>) + sin(<em>A</em>) cos(<em>A</em>) (cos²(<em>A</em>) - sin²(<em>A</em>)))

• factor out sin(<em>A</em>) cos(<em>A</em>)

… = 2 sin(<em>A</em>) cos(<em>A</em>)/(2 cos²(<em>A</em>) - 1) (1 + cos²(<em>A</em>) - sin²(<em>A</em>))

• simplify the last factor using the Pythagorean identity, 1 - sin²(<em>A</em>) = cos²(<em>A</em>)

… = 2 sin(<em>A</em>) cos(<em>A</em>)/(2 cos²(<em>A</em>) - 1) (2 cos²(<em>A</em>))

• rearrange terms in the product

… = 2 sin(<em>A</em>) cos(<em>A</em>) (2 cos²(<em>A</em>))/(2 cos²(<em>A</em>) - 1)

• combine the factors of 2 in the numerator to get 4, and divide through the rightmost product by cos²(<em>A</em>)

… = 4 sin(<em>A</em>) cos(<em>A</em>) / (2 - 1/cos²(<em>A</em>))

• rewrite cos = 1/sec, i.e. sec = 1/cos

… = 4 sin(<em>A</em>) cos(<em>A</em>) / (2 - sec²(<em>A</em>))

• divide through again by cos²(<em>A</em>)

… = (4 sin(<em>A</em>)/cos(<em>A</em>)) / (2/cos²(<em>A</em>) - sec²(<em>A</em>)/cos²(<em>A</em>))

• rewrite sin/cos = tan and 1/cos = sec

… = 4 tan(<em>A</em>) / (2 sec²(<em>A</em>) - sec⁴(<em>A</em>))

• factor out sec²(<em>A</em>) in the denominator

… = 4 tan(<em>A</em>) / (sec²(<em>A</em>) (2 - sec²(<em>A</em>)))

• rewrite using the Pythagorean identity, sec²(<em>A</em>) = 1 + tan²(<em>A</em>)

… = 4 tan(<em>A</em>) / ((1 + tan²(<em>A</em>)) (2 - (1 + tan²(<em>A</em>))))

• simplify

… = 4 tan(<em>A</em>) / ((1 + tan²(<em>A</em>)) (1 - tan²(<em>A</em>)))

• condense the denominator as the difference of squares

… = 4 tan(<em>A</em>) / (1 - tan⁴(<em>A</em>))

(Note that some of these steps are optional or can be done simultaneously)

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Someone help me fast please
lions [1.4K]

Answer:

86

Step-by-step explanation:

<u>Perimeter of WXY = WSY+WRX+XY</u>

<em>--> WSY = SY x 2</em>

--> WSY = 16 x 2 = 32

<em>Since it is an isosceles triangle, WRX = WSY</em>

--> WRX = 32

<em>--> Draw a straight line from W to XY to divide it into two halves assuming it to be point A. This would form a right angle triangle of WAX.</em>

<em>--> Solve it using the cos theta rule</em>

--> Angle = Angle X = 70°

    Hypotenuse = WRX = 32

    Adjacent = WA = ?

<em>--> Cos (Angle) = Adjacent/Hypotenuse</em>

    Cos (70) = WA/32

    WA = 10.9 rounded off to 11

--> WA=AY= 11

--> XY = WA + AY = 11+11 = 22

<em>--> Perimeter = WSY+WRX+XY</em>

    Perimeter = 32+32+22

    Perimeter = 86

Therefore, the perimeter of WXY is 86.

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3 years ago
What times something equals 26
Lunna [17]
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3 0
3 years ago
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What is 5 5/7 * 5 5/7​
hichkok12 [17]

Answer:

1600/49

Step-by-step explanation:

5 5/7 = 40/7

40/7 * 40/7 = 1600/49

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3 years ago
Please!!!! HELP ME!! I give brainlyest!!! are u my friend? The table below models the cost, y, of using a high-efficiency washin
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Answer:

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Step-by-step explanation:

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3 years ago
In a recent survey, 40 percent indicated chocolate was their favorite flavor of ice cream. Suppose we select a sample of twelve
worty [1.4K]

Answer:

4 people name chocolate

Step-by-step explanation:

Let's first understand the given information.

The survey shows that 40 percent of a finite number of people name chocolate as their favorite flavor of ice cream. Because the survey is reporting a percentage, then 40% means that from 100 people 40 people name chocolate, while the others name a different type of flavor.

Dividing the total of people (100) by the ones who name chocolate (40) then we have:

100/40 = 2.5

Through the above equation we are actually expressing the following:

Total people = 2.5 * (people who name chocolate flavor)

Using this equation if we have now 12 people:

12 = 2.5 * (people who name chocolate flavor)

12/2.5 = (people who name chocolate flavor)

4.8 = people who chose chocolate flavor

Because we can't have 0.8 of a person, then if we have a sample of 12 people, we will expect that 4 of them name chocolate.

5 0
3 years ago
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