Answers
This is one pathway to prove the identity.
Part 1
[tex]\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{1}{\tan(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\cot(\theta) = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{\cos(\theta)}{\sin(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)*\sin(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)(1-\cos(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\[/tex]
Part 2
[tex]\frac{\sin^2(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)-\cos^2(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{\sin^2(\theta)-(\cos(\theta)-\cos^2(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{\sin^2(\theta)-\cos(\theta)+\cos^2(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\[/tex]
Part 3
[tex]\frac{\sin^2(\theta)+\cos^2(\theta)-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1}{\sin(\theta)} = \frac{1}{\sin(\theta)} \ \ {\checkmark}\\\\[/tex]
As the steps above show, the goal is to get both sides be the same identical expression. You should only work with one side to transform it into the other. In this case, the left side transforms while the right side stays fixed the entire time. The general rule is that you should convert the more complicated expression into a simpler form.
We use other previously established or proven trig identities to work through the steps. For example, I used the pythagorean identity [tex]\sin^2(\theta)+\cos^2(\theta) = 1[/tex] in the second to last step. I broke the steps into three parts to hopefully make it more manageable.
Related Questions
quick question: is this the way you do this?
Answers
Answer:
Yes, you did really good actually.
Step-by-step explanation:
Helppppp w marhs please
Answers
Answer:
-18a^7
Step-by-step explanation:
When you multiply like bases, you add the exponents.
(3a^4)(-6a^3) =
-18a^7
Answer:
-18a^7
Step-by-step explanation:
hope this helped
Simplify the expression:
3w - 4w + -5W - 6W + -9
Answers
Answer:
-12w - 9
Step-by-step explanation:
[tex]3w - 4w + ( - 5w) - 6w +( - 9) \\ - 1w + ( - 5w) - 6w + ( - 9) \\ - 6w - 6w + ( - 9) \\ - 12w - 9[/tex]
Hope this helps! Brainliest would be really appreciated!
guys pls help me!!!!!!
Answers
Answer:
25
Step-by-step explanation:
Answer:
The answer is 25
Step-by-step explanation:
PLEASE HELPPP QUICK!!
Larry is on his school's cross-country team. He runs 8 miles during each practice.
Write an equation that shows the relationship between the number of practices Larry attends, x, and the total number of miles he runs, y.
Y=
Answers
Answer:
8x=y or y=8x
Step-by-step explanation:
So 8 is the number of hours,
we can interpet x for the amount of practice he goes to. For example if hee goes,
for example if he goes to 2 practices the equation will be =
8(2)=Y.... 8(2)=16
16 is the number of miles he runs for 2 practice
We can insert the number of practice he goes to into X
Help me please I’ll reward you with 5 stars
Answers
Answer:
[tex] \sqrt{18} [/tex]
bc its result equals 4.242640687
Answer:
C [tex]\sqrt{16}[/tex] (Perfect square)
Step-by-step explanation:
Square root of 15 it will be 3.8..but doesn't repeat
Square root of 16 is 4 (perfect square)
Square root of 17 is 4.123... doesn't repeat or stop
Square root of 18 is 4.242.. but doesn't repeat or stop.
--
A rational number can be expressed as a ratio or a fraction.
--
16 can be expressed as a fraction the other numbers keep going meaning never stop.
HELP I NEED AN ANSWER ASAP!!
Answers
Answer:
put them in desmos......
Answer:
can't see the question man take a different picture
5x-7=2x+8 solve for x
Answers
Answer:
x=5
Step-by-step explanation:
Simplifying 5x + -7 = 2x + 8 Reorder the terms: -7 + 5x = 2x + 8 Reorder the terms: -7 + 5x = 8 + 2x Solving -7 + 5x = 8 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -7 + 5x + -2x = 8 + 2x + -2x Combine like terms: 5x + -2x = 3x -7 + 3x = 8 + 2x + -2x Combine like terms: 2x + -2x = 0 -7 + 3x = 8 + 0 -7 + 3x = 8 Add '7' to each side of the equation. -7 + 7 + 3x = 8 + 7 Combine like terms: -7 + 7 = 0 0 + 3x = 8 + 7 3x = 8 + 7 Combine like terms: 8 + 7 = 15 3x = 15 Divide each side by '3'. x = 5 Simplifying x = 5
5x-2x=8+7
3x=15
x=5
what mass is 500 g less than 4,32 kg
Answers
Answer:
Step-by-step explanation:
500g=500g
432kg=43200g
43200-500=42700g
answer 42700g
A ladder which is 4.7 m long is placed on the ground 0.5 m from a vertical wall and then leaned over to the wall.
How high up the wall can the ladder reach?
Give your answer rounded to 1 DP.
Answers
Answer:
the can reach up to 4.6 m
At Rosa's Rose Shop, a bouquet containing a dozen roses costs $20. If the price of a bouquet is directly proportional to the number of roses it contains, how many dollars will a bouquet of 39 roses cost?
Answers
Answer:
It will cost $65.
Step-by-step explanation:
A dozen is 12. To find how much it will cost, we can divide the bouquet by 12.
39 ÷ 12 = 3 r3
with the remainder, we can
12 ÷ 3 = 4
3 is 1/4 of 12.
So we can multiply the price of bouquet by 1/2 to find the remainder's price. The whole equation would look like this:
(3x20) + (1/4 x 12)
60 + (1/4 x 20)
60 + 5
65
The answer is 65.
7. People are migrating from one country or continent to the other in search of a better future. Many factors are being considered in
migration. Suppose x number of Filipinos migrate to Australia, express the following number of people migrating to other continents
(excluding Antarctica).
a. Africa : 20 less than the migration to Australia ( Answer: x - 20 )
b. Asia : 100 more than twice the migration to Australia (2 points)
c. North America : 15 more than 3 times the migration to Australia (2 points)
d. Europe: 10 more than twice the migration to Australia (2 points)
e. South America : 50 more than the migration to Australia (2 points)
f. Find the ratio (using fraction) of the migration to Europe over the migration to North America (Simplify your answer using
factoring) Show your solution. (5 points)
g. If x = 100, which continent has the biggest number of migration? Show your solution from a to e. (7 points)
Answers
Answer:
toyota innova 2.8 G A/T 2021 4x1
PLEASE PLEASE PLEAAAASE HELP! I NEED TO TURN IT IN RIGHT NOW! PRETTY PLEEEASE
Answers
Answer:
5,000,000
Step-by-step explanation:
10 x 10 x 10 x 10 x 10 x 10 = 1,000,000
1,000,000 x 5 = 5,000,000
Answer:
5 Mg
Step-by-step explanation:
The metric prefix associated with [tex]10^{6}[/tex] is Mega (M).
This can be written as 5 Mg.
A, B, C and D are points on the circle, centre O. BCE is a straight line. Angle AOC= 108° and angle DCE= 60°. Calculate the values of w, x and y
Answers
Steps are in the attatchment. My answer to a assignment the same as this.
The cost of feeding a cat during it’s lifetime
Answers
Answer:
The average lifetime cost of owning a cat ranges from $5,000 to $23,000
Answer:
The average lifetime cost of owning a cat ranges from $5,000 to $23,000.
Step-by-step explanation:
hope it helps
mark me brainliest pls
which of the values below will make 3x - 8=40 true
A=14
B=15
c=16
Answers
Answer:
C
Step-by-step explanation:
3x-8=40 write original equation
+8 +8 add 8 to each side
3x=48 simplify
3x/3 48/3 divide
x=16 simplify
Write the product as a power
3*3*3*3
Answers
Just put the four on the top right of the three and make it small
Answer:
3^4
Step-by-step explanation:
[tex]3*3*3*3[/tex] [tex]3^1 * 3 * 3 * 3[/tex] [tex]3^2 * 3 * 3[/tex] [tex]3^3 * 3[/tex] [tex]3^4[/tex]Therefore, the product of 3 × 3 × 3 × 3 written as a power is 3^4.
Please help;-; tysm! you don't gotta explain since its already explaining template
(23 points)
Answers
Answer:
108
108
0410404018404400
5(p+3)=37.95
help me with my homework
Answers
Answer:
p= 4.59
Step-by-step explanation:
Hope this helped :)
What would be the denominator after rationalizing 7/(5√3-5√2)
Please tell fast
I will mark branliest please fast
Thank you ☺️
Answers
Step-by-step explanation:
=> 7/(5√3-5√2) × (5√3+5√2)/(5√3+5√2)
=> 7(5√3+5√2)/75-50
=> (35√3+35√2)/25.
after rationalising the denominator is 25.
hope this helps you.
I need help, please!!
Answers
9514 1404 393
Answer:
f(x) = 0.5x +4
Step-by-step explanation:
The function rule will replace h with f(x), and d with x:
h = 0.5d +4
f(x) = 0.5x +4
__
The table values are found by putting x into the function rule and doing the arithmetic. For example, for x=1, we have ...
f(1) = 0.5·1 +4 = 0.5 +4 = 4.5
The full table and the graph are shown in the attachment.
damon ate lunch at a restaurant.the bill came to 8.33.if he left an 18% tip, how much was the tip
Answers
Answer:
$1.50 was the total tip.
Step-by-step explanation:
Divide the total ($8.33) by 100
multiply the answer (0.0833) by the percentage (18)
you get $1.4994 to be exact, but we will round that to $1.50.
I need help
please help
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Dilation by a factor of 1/2 about point S means each point moves to a position half as far from S as it was to begin with. Point S remains invariant. (Point S and S' are the same point.)
Given the function f(x) = 2x + 5, what would the input be with an output of 21
Answers
Given :-
f(x) = 2x + 5To Find :-
The input when output is 21 .Answer :-
The given function is ,
f(x) = 2x + 5Substitute f(x) = 21 ,
21 = 2x + 521 - 5 = 2x 16 = 2x 16/2=xx = 8Answer:
input = 8
Step-by-step explanation:
x is the input and f(x) is the output
Given f(x) = 2x + 5 and f(x) = 21 , then equating gives
2x + 5 = 21 ( subtract 5 from both sides )
2x = 16 ( divide both sides by 2 )
x = 8
That is the input is 8
Please help me solve this
Answers
Answer:
4
Step-by-step explanation:
so first minus the total food price out..52-18=34
next, divide that by 8.50, you get 4. so four friends went to the movies.
someone please help ASAP
Answers
Answer:
Wilde River
Step-by-step explanation:
If you look at their wins and losses (47 and 11) they will have an 81% chance of winning compared to the other team's 63% chance of winning.
47/58=81
22/35=62.8
I NEED HELP ASAP!!!!!!!!!!!!!!!!
Mrs. Baxter deposits $2,000 in an account that earns 5% simple interest. How much is Mrs. Baxter's investment worth after 8 years?
I need the formula, work, and solution.
Answers
Answer:
3200 i think
Step-by-step explanation:
2,000/5=400
400x8=3200
Answer for 17 please???????????
Answers
The amount of degrees in a polygon: 360
In a pentagon: 360 / 5 = 72
9x - 18 = 72 Add 18 to both sides
9x = 90 Divide by 9
x = 10
f(x)=2x^2+6x-8,g(x)=-3x-3 find the value of g(f(1))?
Answers
Answer:
g(f(1)) = -3
Step-by-step explanation:
First calculate f(1). In order to do that, you have to substitute 1 back into every “x” that you see in the “F” function.
F(1) = 2(1)^2+6(1)-8
= 2+6-8
= 0
f(1) = 0
Now that you’ve figured out that f(1) = 0. You can substitute 0 in order to find the answer to your question.
g(f(1)) = g(0) find g(0) the same way you found f(1)
g(0) = -3(0)-3 = -3
g(f(1)) = -3
What is the inequality shown?
Answers
Answer:
I think it's >-4 subtracted by 3 but I'm not sure