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Tanya [424]
3 years ago
8

Verify the identity. 4 csc 2x = 2 csc2x tan x

Mathematics
1 answer:
vlada-n [284]3 years ago
6 0

Step-by-step explanation:

4csc(2x) = 2csc^2(x) tan(x)

We start with Left hand side

We know that csc(x) = 1/ sin(x)

So csc(2x) is replaced by 1/sin(2x)

4 \frac{1}{sin(2x)}

Also we use identity

sin(2x) = 2 sin(x) cos(x)

4 \frac{1}{2sin(x)cos(x)}

4 divide by 2 is 2

Now we multiply top and bottom by sin(x) because we need tan(x) in our answer

2\frac{1*sin(x)}{sin(x)cos(x)*sin(x)}

2\frac{sin(x)}{sin^2(x)cos(x)}

2\frac{1}{sin^2(x)} \frac{sin(x)}{cos(x)}

We know that sinx/ cosx = tan(x)

Also  1/ sin(x)= csc(x)

so it becomes 2csc^2(x) tan(x) , Right hand side

Hence verified



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70 = -7 k solve the equations
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Answer:

-10

Step-by-step explanation:

70= -7k

70 -7k

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-7 -7

-10=k

Have a great day

4 0
3 years ago
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A 60 inch board is to be cut into three peices so that the second peice is four times as long as the first peice and the third p
Lostsunrise [7]

Answer:

The first piece is 6 inches, the second piece is 24 inches, and the third piece is 30 inches

Step-by-step explanation:

Since the second piece is 4 times longer than the first one, it will be represented by 4x.

The third piece is 5 times as long as the first one, so it will be represented by 5x.

Create an equation adding up the 3 x values up to 60:

x + 4x + 5x = 60

Add like terms and solve for x:

10x = 60

x = 6

So, the first piece is 6 inches.

Then, plug in 6 for x to find the lengths of the second and third pieces.

4x

4(6)

= 24

The second piece is 24 inches

5x

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= 30

The third piece is 30 inches

So, the first piece is 6 inches, the second piece is 24 inches, and the third piece is 30 inches

6 0
3 years ago
A bag contains 4 red marbles,
GuDViN [60]

Step-by-step explanation:

4+6+5=15

15-1=14

2/14

1/7

4 0
3 years ago
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Simplify the following expressions <br> 1/4 (24-16x)<br><br> what is the sum?<br> 7/4 + (-1/5)
Artyom0805 [142]
1.55 i did that math too it was kinda hard but i did it
4 0
2 years ago
The function​ s(t) represents the position of an object at time t moving along a line. Suppose s(2)=150 and s(5)=237. Find the a
trapecia [35]

Answer:

29 is answer.

Step-by-step explanation:

Given that the function​ s(t) represents the position of an object at time t moving along a line. Suppose s(2)=150 and s(5)=237.

To find average velocity of the object over the interval of time [1,3]

We know that derivative of s is velocity and antiderivative of velocity is position vector .

Since moving along a line equation of s is

use two point formula

\frac{s-150}{237-150} =\frac{t-2}{5-2} \\s=29t-58+150\\s=29t+92 gives the position at time t.

Average velocity in interval (1,3)

=\frac{1}{3-1} (s(3)-s(1))\\=\frac{1}{2} [87+58-29-58]\\=29

5 0
3 years ago
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