Prove this

1-tan^2x/1+tan^2x=cos^2x-sin^2x

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the identity

tan x = [tex]\frac{sinx}{cosx}[/tex]

Consider the left side

[tex]\frac{1-tan^2x}{1+tan^2x}[/tex]

= [tex]\frac{1-\frac{sin^2x}{cos^2x} }{1+\frac{sin^2x}{cos^2x} }[/tex] ( multiply numerator and denominator by cos²x to clear fractions

= [tex]\frac{cos^2x-sin^2x}{cos^2x+sin^2x}[/tex] ← ( cos²x + sin²x = 1 ]

= cos²x - sin²x

= right side , thus proven


Related Questions

Can you guys help me find a flag that has at least one reflection and a translation in it? If not, then two flags that show these transformations.

This is very urgent and I need to get it done soon, whoever is willing to help me I'll mark you as brainliest. Thank you!

Answers

Answer:

The united nations flag the translation can be any of the blue triangles and the reflection if the flag itself as it is symmetrical

Step-by-step explanation:

The united nations flag the translation can be any of blue triangles and the reflection if the flag itself as it is symmetrical.

How does reflection across axis work?

When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if we're seeing it in a mirror.

If we study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.

If you're reflecting a point (x,y) along x axis, then its abscissa will stay same but ordinates will negate. Thus (x,y) turns to (x, -y)

Similarly, if you're reflecting a point (x,y) along y axis, the resultant image of the point will be (-x,y)

Therefore, The united nations flag the translation can be any of blue triangles and the reflection if the flag itself as it is symmetrical.

Learn more about reflection;

https://brainly.com/question/12950057

#SPJ2

What are the coordinates of the quadrilateral WXYZ after it is reflected across the y-axis.

Answers

Step-by-step explanation:

the coordinates of the quadrilateral WXYZ after reflected across the y-axis:

W' (3, 4)

X' (-2, 8)

Y' (-4, -4)

Z' (3, -4)

Anyone know the answer?

Answers

Answer:

Step-by-step explanation:

(21 + 3y) + y = 90

21 + 4y = 90

4y = 69

y = 17.25

x = 21 + 3(17.25)

x = 21 + 51.75

x = 72.75

Answer check:

72.75 + 17.25 = 90

90 = 90 Corrrrrrect !

Answer: x = 72.75 and y = 17.25

Explanation:

x = 3y + 21

And x + y = 90° (complementary angle)

Substitute x value in the equation:

3y + 21 + y = 90
4y + 21 = 90
4y = 69
y = 69/4
y = 17.25

x = 3(17.25) + 21
x = 51.75 + 21
x = 72.75

Vie sold 45 raffle ticket. his brother sold twice as many. How many tickets did the sell together?

Answers

Answer:

135 tickets

Step-by-step explanation:

Vie's brother sold twice as many as Vie. So we multiply Vie's tickets by 2 to get the brother's.

VIe's brother sold 45 * 2 = 90 tickets

And all together the two sold

45 + 90 = 135 tickets

6.

For which discriminant is the graph possible?

A. b2 – 4ac = 7
B. b2 – 4ac = 0
C. b2 – 4ac = –12

Answers

Answer:

A. b2 – 4ac = 7

Step-by-step explanation:

Use objects or shapes to describe a a right angle

Answers

Answer:

square because it has 4 90⁰ angles

Compute each of the following values for f (x) = 1/x-2. Step by step
a. f(2.5)
b. f(1.75)
c. f (2)
d. Justify your answer for part (C).​

Answers

Step-by-step explanation:

subtitle values of x one by one:

a)f(2.5)=1/2.5-2

f(2.5)=1/0.5

f(2.5)=2

b)Now x=1.75

f(1.75)=1/1.75-2

f(1.75)=1/-0.25

f(1.75)=-4

c)x=2

f(2)=1/2-2

f(2)=1/0

f(2)=infinity

d)something divided by zero is equal to infinity that is exteremly large value

MARKING BRAINLIEST !! using the distance formula falculate the perimeter of the triangle below
a. 27.9 units
b. 24.3 units
c. 25.7 units
d. 28.2 units ​

Answers

Answer:

a

Step-by-step explanation:

i didn't use the distance formula, instead i used the pythagrean theorum. i counted the units for the legs, and made three smaller triangle and solved them to find the lengths of the hypotenuse and the added the three of those together to find the perimiter of the original triangle

4√6 • √6 = ?
I know this, my brain is just being a turd, someone help please-

Answers

Answer:

This is very simple . you can easily understand. hope it helps.

When p= 12, t= 2, and s= 5, r= 18. If rvaries directly with p and inversely with the product of sand t, what is the
constant of variation?

Answers

Answer:

15

Brainliest, please!

Step-by-step explanation:

r = kp/(st)

p = 12, t = 2, s = 5, r = 18

18 = k(12)/(2)(5)

18 = 12k/10

12k = 180

k = 15

Solve the equation.
3(2x + 7) = - 23 + 14

Answers

Step-by-step explanation:

6x+21=-9

6x=-9-21

x=-30/6

x= -5

Answer:

[tex]3(2x + 7) = - 23 + 14 \\ 6x + 21 = - 9 \\ 6x = - 30 \\ x = \frac{ - 30}{6} \\ x = 5 \\ thnk \: you[/tex]

−5x+4y=3

x=2y−15



what would be the values of x and y

Answers

Answer:

x=9 y=12

Step-by-step explanation:

eqn 1 - x=2y-15

eqn 2- -5x+4y=3

-5(2y-15)+4y=3

-10y+75+4y-3=0

-6y+72=0

y= 12

x=2y-15

x=2(12)-15

x= 9

They gave that -5x+4y=3 and x=2y-15

Substitution,

-5(2y-15) + 4y=3
-10y + 75+ 4y=3
75-3 = 10y - 4y
6y = 72
y. = 72/6
Y= 12

Now find x

X= 2(12) - 15
X= 24 - 15
X= 9

Soo
X= 9; Y= 12

Translate each phrase into a variable expression. Use n for the variable. Five more then a number

Answers

Step-by-step explanation:

I only see one phrase (correcting a typo) : "five more than a number".

that is expressed in math by using "n" for the variable "number " :

n + 5

or

5 + n

as additions and multiplications are commutative, they can be written and executed in any sequence. it is always the same result.

HELP

Write one equation that has solutions of x = -3 and x = 2.​

Answers

Answer:

x = -3

Equation: 2x + 2 = -4

x = 2

Equation: 3x - 3 = 3

What is -0.56 as a fraction in simplest form?
-14/25
-5/6
-56/100
-7/10

Answers

The answer to it is A. -14/25.

ken has 5 lemons and 3 oranges in his shopping trolley and the cost of the fruit is $3.50. Barbie, with 2 lemons and 4 oranges pays $2. 10 for her fruit. how much does each type of fruit cost?

Answers

Answer:

A) 5 L + 3 O = 3.50

B) 2 L + 4 O = 2.10

Multiplying B) by -2.5

B) -5L -10 O = -5.25 then a adding A)

A) 5L + 3 O = 3.50

-7 O = -1.75

Oranges = .25 each

Lemons = .55 each

Step-by-step explanation:

Help ASAP I’ll mark you as brainlister

Answers

Answer:

the range is from 6 to -4 (both inclusive)

Step-by-step explanation:

the domain is all values of x for which the function is defined and the range is all values of y for which the function is defined hence the domain is -3 to -11 and the range is 6 to -4

if f(X+4) =3x+4 , then find the value of f(4)
please explain it clearly .​

Answers

[tex]\\ \sf\longmapsto f(x+4)=3x+4[/tex]

[tex]\\ \sf\longmapsto f(x)=3x+4-4[/tex]

[tex]\\ \sf\longmapsto f(x)=3x[/tex]

Now

[tex]\\ \sf\longmapsto f(4)[/tex]

[tex]\\ \sf\longmapsto 3(4)[/tex]

[tex]\\ \sf\longmapsto 12[/tex]

angle A and angle B are supplementary angles.If m angle A=(7x+15 ^ and m angle B=(2x−3) then find the measure of ∠ A.

Answers

Angle A= 141 degrees

The length and the width of a rectangle are (2x+5) cm and (2x-7) cm respectively. Given that the area of the rectangle is 14cm^2, find its length and width.

Answers

Answer:

Length=13.07 and Breadth=1.07

Step-by-step explanation:

Area=l*b

14=(2x+5)(2x-7)

14=4x^2-4x-35

4x^2-4x-49=0

Using quadratic formula, we have x=(1±5sqrt(2))/2 but as length can't be negative, so x=(1+5*sqrt(2))/2

Length=13.07 and Breadth=1.07

Mr. Mad Scientist earns $152, 200 per year. If he has to pay 15% in Income taxes per year how much money does he have after he pays his taxes for the year? *

Answers

Answer:

he have after he pays his taxes for a year 152185

What is the recursive formula of the geometric sequence?
1∕2, 3∕4, 9∕8, 27∕16, ...

Answers

Step-by-step explanation:

a=1/2, r=9/8÷3/4

=3/2

Tn=ar^n

Answer:

[tex]x_{0} = \frac{1}{2}[/tex]

[tex]x_{n} = x_{n-1} *(\frac{3}{2} )[/tex]

Step-by-step explanation:

Twice a number is forty in equation form

Answers

Answer:

2x = 40

Step-by-step explanation:

Let the number be x

Twice means 2 time

2 × x

2x

The product is 40

2x = 40

Step-by-step explanation:

Twice a number is forty

Let the number be x, then

2×x=40

2x=40

x=40/2

x=20

how do I identify different terms in an equation

Answers

A term can be a signed number, a variable, or a constant multiplied by a variable or variables. Each term in an algebraic expression is separated by a + sign or J sign. In , the terms are: 5x, 3y, and 8. When a term is made up of a constant multiplied by a variable or variables, that constant is called a coefficient. Hope this helps

Evaluate the expression for x = -3 and y = - 4.

2x+2y=__.

Answers

Answer:

-14

Step-by-step explanation:

Substitute the values for the variables.

[tex]2(-3)+2(-4)\\-6-8\\-14[/tex]

Answer:

-14

Step-by-step explanation:

cause you do 2(-3) + 2(-4) = -14

Find the sum of 2√5 AND 4√3 in simplest form. Also, determine whether the result is rational or irrational and explain your answer.

Answers

Answer:

hey why you delete my answers

Use Distributive property to write the expression without parentheses

Answers

Answer:

-4x + 5y

Step-by-step explanation:

-1/6 x 24 x simplifies to -1 times 4x, which is -4x.  -1/6 times -30y simplifies to -1 times -5y, which is 5y.

Answer:

-4x + 5y

Explanation:

- 1/6(24x - 30y) =

-4x + 5y

Multiply - 1/6 by the numbers in parentheses

How do I write 125,740,689 in expanded form and in words

Answers

Answer:

100,000,000 + 20,000,000 + 5,000,000 + 700,000 + 40,000 + 600 + 80 + 9

One hundred twenty five million, seven hundred forty thousand six hundred eighty nine

Step-by-step explanation:




[tex]\tt\huge\red{Please \: help \: me!}[/tex]

Answers

First find Divisor

Two zeros are -3,-2

[tex]\\ \sf\longmapsto x^2-(-3-2)+(-3)(-2)[/tex]

[tex]\\ \sf\longmapsto x^2+5x+6[/tex]

Dividend given by

[tex]\\ \sf\longmapsto x^4-x^3-16x^2+4x+48[/tex]

We know

[tex]\boxed{\sf Dividend=Divisor\times Quotient +Remainder}[/tex]

Remainder is 0

[tex]\\ \sf\longmapsto Dividend=Divisor\times Quotient[/tex]

[tex]\\ \sf\longmapsto Quotient=\dfrac{Dividend}{Divisor}[/tex]

[tex]\\ \sf\longmapsto \dfrac{x^4-x^3-16x^2+4x+48}{x^2+5x+6}[/tex]

[tex]\\ \sf\longmapsto x^2-6x+8[/tex]

Now factor

[tex]\\ \sf\longmapsto x^2-6x+8=0[/tex]

[tex]\\ \sf\longmapsto x^2-4x-2x+8=0[/tex]

[tex]\\ \sf\longmapsto x(x-4)-2(x-4)=0[/tex]

[tex]\\ \sf\longmapsto (x-4)(x-2)=0[/tex]

[tex]\\ \sf\longmapsto x-4=0\:or\:x-2=0[/tex]

[tex]\\ \sf\longmapsto x=4\:or\:x=2[/tex]

Hence all zeros are

2,-2,-3,4

What is (f - g)(x)? f(x) = 3x g(x) = -3x² + 3x Write your answer as a polynomial or a rational function in simplest form.​

Answers

Answer:

3x²

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= 3x - (- 3x² + 3x) ← distribute parenthesis by - 1

= 3x + 3x² - 3x ← collect like terms

= 3x²

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