All categories

1 year ago

Anyone know how to prove these are equal to one another? I also need all the steps.

Mathematics

1 answer:

IrinaVladis [17]1 year ago

6 0

Answer:

Step-by-step explanation:

it can be simplified to $\frac{sec \theta}{cot\theta+tan\theta} =sin\theta$ . if you multiply each side by the denominator, it becomes $sec\theta=\frac{sin^2\theta}{cos\theta} + cos\theta$ since $tan\theta=\frac{sin\theta}{cos\theta}$ and cotan is the reciprocal of that. Because $sec\theta=\frac{1}{cos\theta}$ so multiplying each side gives $1=sin^2\theta+cos^2\theta$ , and $sin^2\theta+cos^2\theta$ is equal to 1.

You might be interested in

Kenji is decorating papers with a total of 15 heart stickers and 12 star stickers for the child he is babysitting. If he wants t

Marina CMI [18]

Answer: The greatest number of pages Kenji can decorate = 3

Step-by-step explanation:

Given: Total heart stickers = 15

Total star stickers =12

If all the papers identical, with the same combination of heart and star stickers and no stickers left over.

Then the greatest number of pages Kenji can decorate = GCD(15,12) [GCD=greatest common divisor]

Since 15 = 3 x 5

12=2 x 2 x 3

GCD(15,12) =3

Hence, the greatest number of pages Kenji can decorate = 3

7 0

3 years ago

Find the altitude and area of an equilateral triangle

Nataliya [291]

If you look at the attached graphic, you will see that the altitude (or height) of an equilateral triangle is:
Height = side length * sq root (3) / 2
Area = side^2 * sq root (3) / 4

4 0

3 years ago

Given the vectors u = <5,-1> and v = <1,12>, find -7u-3v. *

zepelin [54]

You multiply vectors and scalar simply by multiplying each component by that scalar:

$-7u = \langle-35,7\rangle,\quad -3v=\langle -3,-36\rangle$

Finally, you sum two vectors by summing the correspondent coordinates:

$-7u-3v = \langle-35,7\rangle+\langle -3,-36\rangle = \langle-38,-29\rangle$

4 0

3 years ago

Square RSTU is inscribed in circle P. Given the coordinates for the vertices of the square, find the equation of circle P.

svlad2 [7]

Answer:

$(x-2)^2+y^2=20$

Step-by-step explanation:

We want to find the equation of a circle P, and we know that the square RSTU is inscribed in the circle, this means that if we replace the points:

R(0,4) S(6,2) T(4,-4) and U(-2,-2) the equation must be verified.

Then, we have to replace the points in each option to see which one is the correct answer.

Option A: $(x-2)^2+y^2=68$

R(0,4):

$(x-2)^2+y^2=68\\(0-2)^2+4^2=68\\(-2)^2+16=68\\4+16=68\\20\neq 68$

We can see that R doesn't belong to the equation of the circle.

We could replace the rest of the points in the equation, but since we already know that R does not belong to the circle, we already know that it is not the right option.

Option B: $(x+2)^2+y^2=20$

R(0,4):

$(x+2)^2+y^2=20\\(0+2)^2+4^2=20\\2^2+4^2=20\\4+16=20\\20=20$

The point R(0,4) verifies the equation.

S(6,2):

$(x+2)^2+y^2=20\\(6+2)^2+2^2=20\\8^2+4^2=20\\64+16=20\\80\neq 20$

The point S doesn't belong to the equation of the circle, then we already know that this isn't the correct option.

Option C: $(x-2)^2+y^2=20$

R(0,4):

$(x-2)^2+y^2=20\\(0-2)^2+4^2=20\\(-2)^2+16=20\\4+16=20\\20=20$

The point R verifies the equation.

S(6,2):

$(x-2)^2+y^2=20\\(6-2)^2+2^2=20\\4^2+4=20\\16+4=20\\20=20$

The point S verifies the equation.

T(4,-4):

$(x-2)^2+y^2=20\\(4-2)^2+(-4)^2=20\\2^2+16=20\\4+16=20\\20=20$

The point T verifies the equation.

U(-2,-2):

$(x-2)^2+y^2=20\\(-2-2)^2+(-2)^2=20\\(-4)^2+4=20\\16+4=20\\20=20$

The point U verifies the equation.

<em>We can see that the four points RSTU verifies the equation. This means that the square RSTU is inscribed in circle P whose equation is: </em> $(x-2)^2+y^2=20$

<em>We can see that the graph of the equation verifies the answer.</em>

3 0

4 years ago

If it takes 25 liters of gas to drive 150 miles, how many miles can be driven

Gala2k [10]

Answer:210 because 150 divided by 25 is 6 and 35 times 6 is 210

Step-by-step explanation:hope this helps : )

8 0

3 years ago

Read 2 more answers