1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aivan3 [116]
3 years ago
6

Prove the trigonometric identity

Mathematics
1 answer:
Annette [7]3 years ago
4 0

Answer:

Proved See below

Step-by-step explanation:

Man this one is a world of its own :D Just a quick question are you a fellow Add Math student in O levels i remember this question from back in the day :D Anyhow Lets get started

For this question we need to know the following identities:

1+tan^{2}x=sec^2x\\\\1+cot^2x=cosec^2x\\\\sin^2x+cos^2x=1

Lets solve the bottom most part first:

1-\frac{1}{1-sec^2x} \\\\

Take LCM

1-\frac{1}{1-sec^2x} \\\\\frac{1-sec^2x-1}{1-sec^2x} \\\\\frac{-sec^2x}{1-sec^2x} \\\\\frac{-(1+tan^2x)}{-tan^2x}

now break the LCM

\frac{-1}{-tan^2x}+\frac{-tan^2x}{-tan^2x}\\\\\frac{1}{tan^2x}+1\\\\cot^2x+1

because 1/tan = cot x

and furthermore,

cot^2x+1\\cosec^2x

now we solve the above part and replace the bottom most part that we solved with cosec^2x

\frac{1}{1-\frac{1}{cosec^2x} } \\\\\frac{1}{1-sin^2x} \\\\\frac{1}{cos^2x}\\\\sec^2x

Hence proved! :D

You might be interested in
Consider these scenarios. 1. A piano weighs 5.5 × 102 units.   2. A grain of salt weighs 1.02 × 10-3 units.   3. A tractor trail
zhannawk [14.2K]

Answer:

1) pounds

2) grams

3) tons

Step-by-step explanation:

The suitable measurements for the scenarios are:

1) A piano weighs 5.5 × 10² units

  550 Ib (pounds)

2) A grain of salt weighs 1.02 × 10^-3  units

    0.00102 grams

3) A tractor trailer weighs 8.8 × 10^1 units

    88 ton

   

10²g = 1kg

10^-3g = miligrams

10^1 g = decagram

5 0
3 years ago
Read 2 more answers
The amount of money in a saving account increase from $250 to $270 what is the precent increase of the money in the savings acco
saveliy_v [14]

Answer:

8%

Step-by-step explanation:

percent increase = [ (difference between initial value and final value) ÷ initial value] x 100

⇒ percent increase = [ (270 - 250) ÷ 250] x 100 = 8%

7 0
3 years ago
Read 2 more answers
Which of the following is true of algorithms and heuristics for solving real-life problems?
professor190 [17]

Answer: Under the given option, the following is true of algorithms and heuristics for solving real-life problems: <u><em>Heuristics are shortcut strategies. </em></u>

Algorithms are known as step by step plan of action for resolving a issue. It leads to a specific solution, methodically.

whereas;

Heuristics are known as short‐cut, step‐saving reasoning scheme or generalization that bring forth a solution speedily but possibly with an error.

<u><em>Therefore, the correct option is (a)</em></u>

4 0
3 years ago
Simplify. (-4x^4+x^2-4)+(5x^2-4)(−4x ​4 ​​ +x ​2 ​​ −4)+(5x ​2 ​​ −4)
zloy xaker [14]
-4x^4 - 15x^2 + 1 - 19/x^2 is your answer

Hope I helped :)
8 0
3 years ago
In a factory eggs are packaged in groups of 12 per box how many can the factory make 1534 eggs
Marianna [84]
127 boxes is the answer

You just divide the number of eggs by 12

I don’t know if this is what you were asking because the question is worded weirdly
8 0
3 years ago
Other questions:
  • the point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = (x – 12). What is the stand
    5·1 answer
  • 5. Mrs. Parker is providing lunch at her next staff meeting. She will pay $15.75 for 3 people
    11·1 answer
  • Evaluate the following expressions using the order of operations
    14·1 answer
  • I’m really struggling with these questions
    11·1 answer
  • Which of these points lies on the circle with the center (2,3) and radius 2?
    7·2 answers
  • There are 36 carpenters in a crew.
    5·2 answers
  • Georgie earns annual salary of $54,790. If she is paid weekly what is her weekly salary to the nearest cent?
    7·1 answer
  • Yen paid $10.50 for 2.5 pounds of pretzels what price did she pay for each pound pretzels?​
    7·2 answers
  • The corner store sells a super-size granola bar for $4. How much do eleven super-size granola bars cost?
    7·2 answers
  • Yunika downloaded two applications for $2.99 each to her cell phone. The remaining applications that Yunika purchased cost $1.99
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!