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Reptile [31]
3 years ago
8

Find the integration of (1-cos2x)/(1+cos2x)

Mathematics
1 answer:
slega [8]3 years ago
8 0

Given:

The expression is:

\dfrac{1-\cos 2x}{1+\cos 2x}

To find:

The integration of the given expression.

Solution:

We need to find the integration of \dfrac{1-\cos 2x}{1+\cos 2x}.

Let us consider,

I=\int \dfrac{1-\cos 2x}{1+\cos 2x}dx

I=\int \dfrac{2\sin^2x}{2\cos^2x}dx         [\because 1+\cos 2x=2\cos^2x,1-\cos 2x=2\sin^2x]

I=\int \dfrac{\sin^2x}{\cos^2x}dx

I=\int \tan^2xdx                      \left[\because \tan \theta =\dfrac{\sin \theta}{\cos \theta}\right]

It can be written as:

I=\int (\sec^2x-1)dx             [\because 1+\tan^2 \theta =\sec^2 \theta]

I=\int \sec^2xdx-\int 1dx

I=\tan x-x+C

Therefore, the integration of \dfrac{1-\cos 2x}{1+\cos 2x} is I=\tan x-x+C.

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4000
Airida [17]

Answer:

$1000 ; 500 ; 1000 ; y = 500x + 1000

Step-by-step explanation:

From the graph, the initial deposit which started the savings account is $1000 ; this is the value on the y - intercept, the value in the account at time or period = 0.

The slope :

x1 = 0 ; y1 = 1000

x2 = 6 ; y2 = 4000

Slope = Rise / Run

Rise = y2 - y1 = 4000 - 1000 = 3000

Run = x2 - x1 = 6 - 0 = 6

Hence,

Slope = 3000 / 6

Slope = 500

y - intercept = 1000 (from. Graph)

Equation in slope intercept form:

General form : y = mx + c

m = slope ; c = intercept

Equation is written as ;

y = 500x + 1000

5 0
3 years ago
Write an equation of a line that is parallel to the line whose equation is 3y=x+6 and that passes through the point (-3,4).
Monica [59]
The standard form of this equation is

y=\frac{1}{3}x+2

The slope of two parallel lines i the same, so the slope of the line we're looking for is also \frac{1}{3}

Since the line passes through (-3,4), the equation is:

(y-4)=\frac{1}{3}(x+3)

\boxed{y=\frac{1}{3}x+5}





3 0
3 years ago
Linda cut a piece of wood for project the first cut is Shawn and can be represented by the equation Y=1/4x-5 Lisa can’t cut need
GuDViN [60]

Lisa's cut will be represented by the equation y = 1/4x + 4


6 0
3 years ago
Read 2 more answers
Please put a serious answer
aksik [14]

Answer:

x=12

Step-by-step explanation:

9x-14=2(3x+11)

9x-14=6x+22

9x-6x=22+14

3x=36

x=36/3=12

8 0
3 years ago
Use the distributive property to express 15+45
Nuetrik [128]
<u><em>Answer:</em></u>
15(1+3)

<u><em>Explanation:</em></u>
<u>The distributive property can be generally expressed as follows:</u>
ab + ac = a(b+c)

<u>The given expression is:</u>
15 + 45

<u>We know that:</u>
15 = 1*15
45 = 3*15

<u>Therefore, the given expression can be written as:</u>
1*15 + 3*15

<u>Taking 15 as a common factor and applying the above rule, we will reach the following expression:</u>
15(1+3)

Hope this helps :)
5 0
3 years ago
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