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

Answers

Answer 1

Answer: $(1+cos\alpha)/(sin\alpha)+(sin\alpha)/(1+cos\alpha)=2cosec\alpha\n\nL=((1+cos\alpha)(1+cos\alpha)+sin\alpha\cdot sin\alpha)/(sin\alpha(1+cos\alpha))=(1+2cos\alpha+cos^2\alpha+sin^2\alpha)/(sin\alpha(1+cos\alpha))\n\n=(1+2cos\alpha+1)/(sin\alpha(1+cos\alpha))=(2+2cos\alpha)/(sin\alpha(1+cos\alpha))=(2(1+cos\alpha))/(sin\alpha(1+cos\alpha))\n\n=(2)/(sin\alpha)=2\cdot(1)/(sin\alpha)=2cosec\alpha=R$

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Need help with both question. Grateful for any help. Thanks
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a childrens book has dimensions 20cm by 24cm what scale factor should be used to make a enlarged version that has dimensions 25cm by 30cm

the population of masterton was 23 000 in 2012. Assume that Masterton population increases at a rate of 2% per year. Write an equation to model the population of masterton (y) based on number of years since 2012(x)

Answers

So, after a year, the population will be

23 000*1.02 (which is 23460 people).

And after two years it will be:

23460*1.02, which is 23930 people. Another way of writing it is
23000*1.02*1.02

so we can generalize: the population of the town, y= 23 000* $1.02 ^(x)$

where x is the number of years passed

An albatross is a large bird that can fly 600 kilometers in 15 hours at a constant speed. Using LaTeX: dd for distance in kilometers and LaTeX: tt for number of hours, an equation that represents this situation is LaTeX: d=40td = 40 t . What are two constants of proportionality for the relationship between distance in kilometers and number of hours?

Answers

Answer:

The constant is 40

Step-by-step explanation:

According to the question we are given an equation that represents the given situation as d = 40t where;

d is the distance in km

t is the time in seconds.

The given function is a direct proportionality. For example if p is directly proportional to q, this is expressed as p ∝ q where ∝ is the proportionality sign. In order to remove the sign we will introduce a constant say "k". The equation will become;

p = kq (p and q are the variables)

A direct proportionality means that as a variable is increasing, the other is increasing and vice versa. Comparing p = kq with d = 40t, we can see that k is equal to 40 and d is directly proportional to t

Hence the constants of proportionality for the relationship between distance in kilometers and number of hours is 40 on comparing.

6. The lengths of two sides of a triangle are 5 cm and 8 cm. Between what two measuresshould the length of the third side fall

Answers

Answer:

triangle inequality: the sum of the length of two sides of a triangle must always be greater than the length of the third side.

we know 2 sides whose sum = 5+8 = 13cm

the 3rd side must be <13 included

the length of the third side must be less than 13 cm, i.e. between 1 and 13 (it cannot be equal to 0 because in this case it does not exist)

on Tuesday elena completed 20 item of her math homework in 36 minute. at that same rate how long will it take her to complete 35 item for Wednesday math homework A.71 minute b.63 minute c. 41 minute d. 35 minute

Answers

H=Homework item(s)

-----------------

20H=36

So what is 35H?

--------------------

20H=36

H=36/20

H=18/10=9/5

----------------------

When H=9/5,

35H

=35*9/5

=315/5

=63

----------------------

* The answer is 63 minutes.

Allison has a poster that is 15 in by 18 in. What will the dimensions of the poster be if she scales it down by a factor of 1/3 ?

Answers

Answer:

Answer 4 : 5in by 6in

Step-by-step explanation:

15 times 1/3 is 5.

18 times 1/3 is 6.

Hope I helped!!

Find the x-coordinates where f '(x) = 0 for f(x) = 2x + sin(2x) in the interval [0, 2π]. so far I found f'(x)=2cos(2x)+2 cos(2x)=-1

Answers

The solutions of the equation $f\left( x \right) = 2x + \sin \left( {2x} \right)$ in the interval $\left[ {0,2\pi } \right]$ are $\boxed{\left( {(\pi )/(2),\pi } \right)}$ and $\boxed{\left( {\frac{{3\pi }}{2},3\pi } \right)}.$

Further explanation:

Given:

The function is $f\left( x \right) = 2x + \sin \left( {2x} \right).$

The first derivative is zero.

Explanation:

The given function is $f\left( x \right) = 2x + \sin \left( {2x} \right).$

Differentiate the function with respect to $x$ .

$\begin{aligned}f'\left( x \right) &= 2 + 2\cos \left( {2x} \right)\n&= 2\left( {1 + \cos 2x} \right)\n\end{aligned}$

Substitute $0$ for $f'\left( x \right).$

$\begin{aligned}2\left( {1 + \cos 2x} \right) &= 0 \n1 + \cos 2x &= 0\n\cos 2x &= - 1\n2x &= {\cos ^( - 1)}\left( { - 1} \right)\n2x &= \frac{{\left( {2n - 1} \right)\pi }}{2} \n\end{aligned}$

In the interval $\left[ {0,2\pi } \right]$ the x-coordinates are $\boxed{(\pi )/(2)}{\text{ and }}\boxed{\frac{{3\pi }}{2}}.$

Learn more:

Learn more about inverse of the function brainly.com/question/1632445.
Learn more about equation of circle brainly.com/question/1506955.
Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Application of derivatives

Keywords: derivative, x – coordinates, interval, far, 2x, sin2x, coordinates, 0, 2pi, y-coordinate.

From there, you simply need algebra and a calculator that works in radians.

Take the inverse cos of both sides to get 2x = arccos(-1)

Then divide both sides by 2 to get x = arccos(-1) / 2

Put that into a calculator and you get π/2. But because your bounds are 0 to 2π, you have to add π your solution to get the solution on the other side of the unit circle, which would be (3π/2).

Now that you have the x value, put (π/2) and (3π/2) into f(x) to get the y coordinate.

f(π/2) = 2(π/2) + sin(2(π/2) = π, which means this solution is just (π/2, π)
f(3π/2 = 2(3π/2) + sin(2(3π/2) = 3π, which means this solution is (3π/2, 3π)

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