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2 years ago

Prove that sinA-sin3A+sin5A-sin7A/cosA-cos3A-cos5A+cos7A= cot2A

1 answer:

4 0

Write the left side of the given expression as N/D, where
N = sinA - sin3A + sin5A - sin7A
D = cosA - cos3A - cos5A + cos7A
Therefore we want to show that N/D = cot2A.

We shall use these identities:
sin x - sin y = 2cos((x+y)/2)*sin((x-y)/2)
cos x - cos y = -2sin((x+y)/2)*sin((x-y)2)

N = -(sin7A - sinA) + sin5A - sin3A
= -2cos4A*sin3A + 2cos4A*sinA
= 2cos4A(sinA - sin3A)
= 2cos4A*2cos(2A)sin(-A)
= -4cos4A*cos2A*sinA

D = cos7A + cosA - (cos5A + cos3A)
= 2cos4A*cos3A - 2cos4A*cosA
= 2cos4A(cos3A - cosA)
= 2cos4A*(-2)sin2A*sinA
= -4cos4A*sin2A*sinA

Therefore
N/D = [-4cos4A*cos2A*sinA]/[-4cos4A*sin2A*sinA]
= cos2A/sin2A
= cot2A

This verifies the identity.

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Which statements correctly describe the cosine and sine functions? Check all that apply. The cosine function increases on (90°,

Jet001 [13]

Answer:

The three correct answers are B "The sine function increases on (0°, 90°) and (270°, 360°)." , E "Both the cosine and sine functions have a maximum value of 1.", and F "Both the cosine and sine functions are periodic."

Step-by-step explanation:

Hope this helps <3

4 0

2 years ago

Here are the ingredients to make 12 cupcakes.

scoundrel [369]

Answer:

Mark needs 2 kg butter, 2 kg caster sugar, 14 eggs, and 1.5 kg flour.

Step-by-step explanation:

Alright, first you double the number of kids, as Mark wants each kid to have two cupcakes, not one. (Then add 80+80 to get 160)

Now add the adults to children: 160+152=312

now divide by 12 to see how many batches of cupcakes he needs to make.

312÷12=26 So he needs to make 26 batches

Now here are the ingredients needed to make 12 batches of cupcakes (I multiplied the amount of each ingredient by 26)

5200 g (5.2 kg) butter, 5200 g (5.2 kg) caster sugar, 104 eggs, and 6500 g (6.5 kg) flour.

now make the measurements the same as Mark's ingredients (or the other way around)

(to save time I am not showing each one, just the normal ingredients turned into kg and compared)

5 kg butter < 5.2 kg butter

5 kg caster sugar < 5.2 kg butter

90 eggs < 104 eggs

5 kg flour < 6.5 kg flour

Now do a little subtraction.....

5.2 kg-5 kg = 2 kg butter is needed....

5.2 kg - 5 kg = 2 kg caster sugar is needed....

104 - 90 = 14 eggs needed....

6.5 kg - 5 kg = 1.5 kg flour needed....

And there you go!!! Hope this helped!!! :D

4 0

2 years ago

(Ross 5.15) If X is a normal random variable with parameters µ " 10 and σ 2 " 36, compute (a) PpX ą 5q (b) Pp4 ă X ă 16q (c) PpX

pochemuha

Answer:

(a) 0.7967

(b) 0.6826

(d) 0.9525

(e) 0.1587

Step-by-step explanation:

The random variable X follows a Normal distribution with mean μ = 10 and variance σ² = 36.

(a)

Compute the value of P (X > 5) as follows:

$P(X>5)=P(\frac{x-\mu}{\sigma}>\frac{5-10}{\sqrt{36}})\\=P(Z>-0.833)\\=P(Z$

Thus, the value of P (X > 5) is 0.7967.

(b)

Compute the value of P (4 < X < 16) as follows:

$P(4$

Thus, the value of P (4 < X < 16) is 0.6826.

(c)

Compute the value of P (X < 8) as follows:

$P(X$

Thus, the value of P (X < 8) is 0.3707.

(d)

Compute the value of P (X < 20) as follows:

$P(X$

Thus, the value of P (X < 20) is 0.9525.

(e)

Compute the value of P (X > 16) as follows:

$P(X>16)=P(\frac{x-\mu}{\sigma}>\frac{16-10}{\sqrt{36}})\\=P(Z>1)\\=1-P(Z$

Thus, the value of P (X > 16) is 0.1587.

**Use a z-table for the probabilities.

8 0

2 years ago

Last week Malia spent $13,000 on advertising. This week, she plans to spend three times as much. Next week, she wants to spend 6

PSYCHO15rus [73]

Answer:

31200 dollars

Step-by-step explanation:

you multiply 13 by 4, because its last week and this week, then find 60 percent of that. Proportion: x/52000=60/100. When solved, it is $31200

4 0

2 years ago

A starting carpenter can build a rough table in 1 hour, and a rough chair in 45 minutes. A finishing carpenter can finish each t

Delvig [45]

Answer:

I believe it is b

Step-by-step explanation:

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2 years ago