Prove that sin²α + cos²α = 1 and [tex]\frac{1}{cos^{2}\alpha }[/tex] = 1 + tan²α
![Prove That Sin + Cos = 1 And [tex]\frac{1}{cos^{2}\alpha }[/tex] = 1 + Tan](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/2HtQ2dtlC2fNAFTIgimcqe31cSnvJgPc.png)
Answers
Answer:
See Explanation
Step-by-step explanation:
[tex] { \sin}^{2} \alpha + { \cos}^{2} \alpha = 1 \\ \\ LHS = { \sin}^{2} \alpha + { \cos}^{2} \alpha \\ \\ = \cancel {\sin}^{2} \alpha + { 1 -\cancel{ \sin}}^{2} \alpha \\ \\ = 1 \\ \\ = RHS \\ \\ \\ \frac{1}{ { \cos}^{2} \alpha } = 1 + { \tan}^{2} \alpha \\ \\ LHS = \frac{1}{ { \cos}^{2} \alpha } \\ \\ = { \sec}^{2} \alpha \\ \\ = 1 + { \tan}^{2} \alpha \\ \\ = RHS[/tex]
Related Questions
Please Show steps to solve x2 + 2x = 4
Its a Perfect Square trinomial.
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A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting
parabola is (4,6). What is the vertex of the function defined as g(x) = f(-2) 2?
Answers
Answer:
5
Step-by-step explanation:
This is because
Answer:
(−2,−6)
Step-by-step explanation:
i got it right
Which of the following congruence statements must be true based on the diagram shown?
Multiple Choice: (Select Two Correct Answers)
A. ∠V≅∠U
B. ∠T≅∠W
C. ∠S≅∠X
D. TU¯¯¯¯¯¯¯≅XW¯¯¯¯¯¯¯¯¯¯
E. ST¯¯¯¯¯¯¯≅VX¯¯¯¯¯¯¯¯
Answers
Tom spent 143 dollars on his shopping spree, he
bought 7 books, after buying them he also bought 17
dollars worth of candy. How much did each book
cost?
Help pls
Answers
Answer:
ii guess 18
Step-by-step explanation:
One book costs $18.
Step-by-step explanation:First, we need to make this into an equation, if we take [tex]x[/tex] = 1 book, we could write it like this :[tex]7x + 17 = 143[/tex]
Then, solve the equation :[tex]7x + 17 = 143[/tex]
(minus 17 on both sides)
[tex]7x = 126[/tex]
(divide both sides by 7)
[tex]x = 18[/tex]
This means that each book cost $18.A 4-column table with 4 rows. Column 1 is labeled Service with entries Restaurant, Florist, Cab Fare, Dog Groomer. Column 2 is labeled Cost with entries 40 dollars, 94 dollars, 32 dollars, 62 dollars. Column 3 is labeled Gratuity with entries 18 percent, 12 percent, 20 percent, 26 percent. Column 4 is labeled Tax with entries 8.5 percent, 12 percent, 0 percent, 5.75 percent.
Approximate the amount of tip for the florist by rounding the cost and the percent gratuity to the nearest ten.
$
Answers
Answer:so what is it 8 or 4 i need help send help for homework
Step-by-step explanation:
work out of angle x 65,45
Answers
Answer:
Calculating an angle. The three trigonometric ratios can be used to calculate the size of an angle in a right-angled triangle. Example. Calculate the angle QPR.
Step-by-step explanation:
The value of x is 70°.
What is a triangle?A triangle is a polygon with 3 sides.
Given that, the measures of the two angles of the triangle are 65° and 45°.
The sum of the interior angles of a triangle is 180°, therefore, it follows:
65° + 45° + x = 180°
110° + x = 180°
x = 180° - 110°
x = 70°
Hence, the value of x is 70°.
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What is the solution to the system of equations?
y=1/2x-6
x=-4
O (8,4)
O (4, -8)
O (4,4)
O (4,-4)
Answers
Answer:
(-4,-8)
Step-by-step explanation:
The solution to the system of equations is,
⇒ (- 4, - 8)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expressions are,
⇒ y = 1/2x - 6
⇒ x = - 4
Now, We can simplify the expression for y as;
⇒ y = 1/2x - 6
Put x = - 4;
⇒ y = 1/2 × - 4 - 6
⇒y = - 2 - 6
⇒ y = - 8
Thus, The solution to the system of equations is,
⇒ (- 4, - 8)
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I REALLY NEED HELP THIS IS DUE TODAY AND IT'S 1:57 PLEASE HELP!!!!
-6 X ?= -18
-2 x ? = 20
-? x -10=-70
-7 x ?= -28
-? x -7= 49
-3 x ? =21
Answers
Simplify : 14z + 8y - 5 + 9y - 10z
Find the Unit Rate: Allison bought 6 pounds of bananas for $10.50. *
Answers
unit rate- 1.75 dollars
Answer:
4z+17y-5
unit rate- 1.75 dollars
Step-by-step explanation:
Welcome
What is the value of x?
(The last picture was blackoops)
Answers
Answer:
38°
Step-by-step explanation:
Every triangle has 180°. This means that all the angles must sum 180°.
[tex](3x-16)+(x+6)+x=180\\3x-16+x+6+x=180\\5x-10=180\\5x=180+10\\5x=190\\x=\frac{190}{5}\\x=38[/tex]
Find the slope and the y intercept of the linear equation y=1/8x +3
Answers
m = slope, b = y intercept
Slope: 1/8, y intercept: 3
pls help asap. due today, will give brainliest
Answers
Answer:
4
Step-by-step explanation:
The first is by Angle - Side - Side
The second is by Angle - Angle - Side
The third one is by Side - Angle - Side
The forth is by Side - Side - Side
Plis reply fast and get brainless
Answers
Answer:
number 1 - 2 is bigger ----- Number 2 - 1 is bigger ------ Number three - 5 is bigger
Step-by-step explanation:
What’s the answer to x
Answers
Answer:
x = 55
Step-by-step explanation:
a triangle's angles must equal when added up to 180.
so
76 + 49 + x = 180
combine terms
125 + x = 180
x = 55
The distance between two points on a coordinate grid is 5 units. One of the points is at (2, -1). The x-coordinate of the other point is -2. Which is a possible value for the missing y-coordinate?
4
2
-2
0
Answers
Answer:
4
Step-by-step explanation:
Fresh peaches are on sale for $2.25 per pound. Greta buys 22 pounds (x) for $$4.50 (y).
What is the equation in standard form that represents this situation?
Answers
Answer:
Each pound of peaches costs $2.25
Then we can define:
x = number of pounds someone buys
y = cost for the x peaches.
So if you buy x pounds of peaches, you will pay x times $2.25
Then we have the relation:
y = x*$2.25
If Greta buys 22 pounds, then we have x = 22
y = 22*$2.25 = $49.50
The cost of buying 22 pounds of peaches is $49.50
Just enter the price, no labels.
Best Buy purchased 60 TV's. They gave away three in a contest, and sold the rest at twice the price that they paid for them. The store's total profit was $11,340.
How much did Best Buy sell each TV for?
Answers
Subtract 3 TVs from 60.
Determine if the following system of equations has no solutions, infinitely many
solutions or exactly one solution.
x + 6y = -5
3x + 18y = -15
Will make brainliest
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Why am I using negative numbers in 6th grade science?
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Answer:
Try stopping at nothing to avoid them
Are the two triangles below similar??
Answers
Answer:
Yes
Step-by-step explanation:
If you find the value of all the angles, you'll find that both triangles' angles are 50, 35, and 90 degrees.
(all the angles in a triangle add up to 180)
NEED HELP………………………………………
Answers
Answer:
5.625
Step-by-step explanation:
Answer:
$8.75
Step by Step Explanation:
10.00 - 1.25= $8.75
Find the area of each triangle to the nearest tenth
Answers
Use the distributive property to write an equivalent expression.
7(1 – 10s + 8)
Answers
Answer:
The answer is = −70s+63
Step-by-step explanation:
7(1−10s+8)
=(7)(1+−10s+8)
=(7)(1)+(7)(−10s)+(7)(8)
=7−70s+56
=−70s+63
Plz help I’m getting timed
Answers
id say its a rhombus. all the other shapes can have right angles
Answer:
rhombus
Step-by-step explanation:
Cedrick has $50 to buy pizza and soda for a birthday party. Each pizza, p, costs $8 and each 2 liter bottle of soda, s, costs $1.25
Which of the following inequalities represent the number of pizzas and sodas Cedrick can buy?
Answers
Answer:
c
Step-by-step explanation:
i need help asap
A scale on a blue print drawing of a house shows that 10 centimeters represents 2 meters
What number of actual meters are represented by 18 centimeters on the blue print
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Answer:
divide 10 2 and 18 to see the blue print centimeters
Please answer correctly will mark brainliest for the correct answer and will follow too ;)
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Answer:
Concept: Perimeter & Rectangle Figures
To find the perimeter you add up all the sides.You are missing EF & FGHence AB=DC= 14M Similarly AD = BC= 11M Now we have all the information we need so we add up all the sides.11+ 7+5+7+6+14= 50 unitsAnswer:
50m ......
Step-by-step explanation:
2(11+14)=2(25)=50 m
=11+14+6+5+7+7
if 25% of 150 is 700% of n, then n is equal to what number
Answers
Please feel free to correct me if I’m wrong! :)
Have a good day!!!!
Answer:
n=75/11
Step-by-step explanation:
good luck
In which choice is y a nonlinear function of x?
O A. y = x/4 + 5
O B. y = 10 + x
O C. y = x+3/4 - 2x
D. y = 2 /x-3 + 5
Answers
Answer:
Option D
Step-by-step explanation:
For a function to be linear, the index of x should be 1. In D the coefficient of x is -1. Therefore D cannot be linear
The variable y a nonlinear function of x in (d) y = 2 /x-3 + 5
How to determine the nonlinear functions?A linear function is represented as:
y = mx + c
Other forms of equation are nonlinear functions
From the list of options, the equation y = 2 /x-3 + 5 do not have the form y = mx + c
Hence, the variable y a nonlinear function of x in (d) y = 2 /x-3 + 5
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Find the value of x. X = ?
Answers
Answer:
[tex] \sqrt{ \frac{9}{2} } [/tex]
Answer:
[tex]x = \sqrt{70} [/tex]
Step-by-step explanation:
Please see the attached pictures for the full solution.
