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3 years ago

Prove that 1+cosA/sinA + sinA/1+cosA=2cosecA

1 answer:

5 0

$\frac{1+cos\alpha}{sin\alpha}+\frac{sin\alpha}{1+cos\alpha}=2cosec\alpha\\\\L=\frac{(1+cos\alpha)(1+cos\alpha)+sin\alpha\cdot sin\alpha}{sin\alpha(1+cos\alpha)}=\frac{1+2cos\alpha+cos^2\alpha+sin^2\alpha}{sin\alpha(1+cos\alpha)}\\\\=\frac{1+2cos\alpha+1}{sin\alpha(1+cos\alpha)}=\frac{2+2cos\alpha}{sin\alpha(1+cos\alpha)}=\frac{2(1+cos\alpha)}{sin\alpha(1+cos\alpha)}\\\\=\frac{2}{sin\alpha}=2\cdot\frac{1}{sin\alpha}=2cosec\alpha=R$

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cricket20 [7]

X=2
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2 years ago

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Which of the following is true for f(x)= -2sin(x)-3?

serious [3.7K]

Let's write the general form of the sine curve:

$f(x)=AsinB(x+C)+D$ , where,

A is the amplitude. Also, if A is negative, curve reflects about x axis
B is the compression/stretching factor. It changes the period when it is a value other than 1.
C is the phase shift. It translates curve left or right. Negative value shifts right and positive value shifts left.
D is the vertical shift. It translates curve up or down. Negative value shifts down and positive value shifts up.

Let's check the 4 choices.

Since this curve's A is -2, its amplitude is 2 and range is from -2 to 2. BUT since D value is -3, it shifts vertically 3 units down making the range from -1 to -5. Clearly choice A is not true.

This graph is the graph of $f(x)=-2sin(x)$ shifted 3 units DOWN since D is negative. This choice isn't true.

Because of the - (minus) sign in front of the function, the function is reflected about x-axis, but amplitude doesn't change. Since A value is 2, amplitude is 2. This is true.

Period depends on the B value. Here, B value is 1, so period is normal as the parent function of a sine curve, which is $2\pi$ , NOT $4\pi$ . So this is not correct.

ANSWER: C is true

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3 years ago

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Evaluate the dot product of (6,-3) and (8,5).

AlladinOne [14]

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4 years ago

A juice stand in Montreal sells a quart of orange juice for 4.40CAN. If 1USD = 1.06CAN and 4 cups = 1 quart, how much will one c

Arte-miy333 [17]

Answer:

A cup of juice will cost 1.04 US dollars

Step-by-step explanation:

Here, we want to know the cost of one cup of juice in US dollars.

The cost of a quart of juice is Canada is 4.40CAN

now, since there are 4 cups in a quart, the cost of a cup of juice will be 4.40/4 = 1.10 CAN

Moving on;

We are told that 1 USD = 1.06 CAN ;

thus x usd = 1.10 CAN

1 * 1.10 = x * 1.06

x = 1.10/1.06

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3 years ago

Find the area of the circle to the nearest whole number, if necessary!

astra-53 [7]

Answer:

The circle has an area of about 1385 square mm.

Step-by-step explanation:

Let's recall that circles have an area that can be found with the following formula:

$A=\pi r^{2}$

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So, to the nearest whole number, the area of the circle is 1385 square mm.

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2 years ago