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Reptile [31]
2 years ago
8

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

Mathematics
1 answer:
slega [8]2 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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A store buys items at a wholesale price of $45 each. If the store marks up the price, and no discounts are given, which could be
jeyben [28]

Answer:

49 and 65

Step-by-step explanation:

when a price is marked up it is greater than the original

7 0
2 years ago
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The circumference of a circle is approximately 131.88 centimeters What is the area of the shaded region (6/10 of a circle)
scZoUnD [109]

Answer:

82.97cm^2

Step-by-step explanation:

Given data

Circumference=  131.88 centimeters

We want to find the area of 6/10 part of a circle

Firstly, let us find the area of the circle

We need to get the radius

C= 2πr

131.88= 2*3.142*r

131.88=6.284r

r=  131.88/6.284

r=20.98 cm

Area= πr^2

Area= 3.142*20.98^2

Area= 3.142*440.16

Area= 1382.98cm^2

Hence 6/10 of a 1382.98

=0.06*1382.98

=82.97cm^2

4 0
2 years ago
it looks as though you made 72 of your goal so far for the month you only have 5 days left to reach 100% of your goal let me rem
dezoksy [38]
72% can also be written as 0.72, so take 0.72 x 45 = 32.4     

Subtract 32.4 from 45    45 - 32.4 = 12.6    You need 12.6 renewals in 5 days.
8 0
3 years ago
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An ice cream store sells 28 flavors of ice cream. Determine the number of 4 dip sundaes.
katrin [286]

Answer:

20,475\ ways

Step-by-step explanation:

we know that

<u><em>Combinations</em></u> are a way to calculate the total outcomes of an event where order of the outcomes does not matter.

To calculate combinations, we will use the formula

C(n,r)=\frac{n!}{r!(n-r)!}

where

n represents the total number of items

r represents the number of items being chosen at a time.

In this problem

n=28\\r=4

substitute

C(28,4)=\frac{28!}{4!(28-4)!}\\\\C(28,4)=\frac{28!}{4!(24)!}

simplify

C(28,4)=\frac{(28)(27)(26)(25)(24!)}{4!(24)!}

C(28,4)=\frac{(28)(27)(26)(25)}{(4)(3)(2)(1)}

C(28,4)=20,475\ ways

5 0
2 years ago
Figure ABCD is a parallelogram. What is the value of n?
Zigmanuir [339]

Answer

Find out the what is the value of n.

To prove

By using the parallelogram property .

In parallelogram opposite angels are congruent .

As shown in the figure .

∠B = ∠ D

As given

∠B = (2n + 32)°

∠D = (4n - 2)°

(2n + 32) =  (4n - 2)

solving the above

4n -2n = 32 +2

2n = 34

n = \frac{34}{2}

n = 17

Therefore the value of n is 17 .


5 0
3 years ago
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