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
Elodia [21]
2 years ago
8

Show that √(1-cos A/1+cos A) =cosec A - cot A​

Mathematics
1 answer:
Gennadij [26K]2 years ago
5 0

Hi there!

\sqrt{\frac{1-cosA}{1+cosA}} =

We can begin by multiplying by its conjugate:

\sqrt{\frac{1-cosA}{1+cosA}} * \sqrt{\frac{1+cosA}{1+cosA}}  = \\\\\sqrt{\frac{(1-cosA)(1 + cosA)}{(1+cosA)(1 + cosA)}} =

Simplify using the identity:

1 - cos^2A = sin^2A

\sqrt{\frac{(1-cos^2A)}{(1+cosA)^2}} =\\\\\sqrt{\frac{(sin^2A)}{(1+cosA)^2}} =

Take the square root of the expression:

{\frac{sinA}{1+cosA} =

Multiply again by the conjugate to get a SINGLE term in the denominator:

{\frac{sinA}{1+cosA} * {\frac{1-cosA}{1-cosA} =\\

Simplify:

{\frac{sinA(1-cosA)}{1-cos^2A} =

Use the above trig identity one more:

{\frac{sinA(1-cosA)}{sin^2A} =

Cancel out sinA:

{\frac{(1-cosA)}{sinA}  =

Split the fraction into two:

{\frac{1}{sinA}   - \frac{cosA}{sinA} =

Recall:

1/sinA = cscA\\\\cosA/sinA = cotA

Simplify:

\frac{1}{sinA} + \frac{cosA}{sinA} = \boxed{cscA - cotA}

You might be interested in
Two line are ___ if and only if they lie in the same plane and do not intersect, and two lines are __ if and only if they lie in
Vilka [71]

the answer is C, I think because parallel lines never touch

6 0
3 years ago
PLEASE HELP ITS DUE SOON IM SO CONFUSED! HELP NEEDED!!
ddd [48]

Answer:

<u>e</u>

Step-by-step explanation:

According to Angle Sum Property :

<u>∠A + ∠B + ∠C = 180°</u>

<u />

============================================================

Given :

⇒ ∠A = 50°

⇒ ∠B = 32°

===========================================================

Solving :

⇒ 50° + 32° + ∠C = 180°

⇒ ∠C + 82° = 180°

⇒ ∠C = <u>98°</u>

6 0
2 years ago
I need serious help grades go in tonighttt
attashe74 [19]
Rewrite it from least to greatest and set it up like shown

8 0
2 years ago
four students have to give a speech in class today. In how many different orders can they give their speeches?
bulgar [2K]

Answer:

There are 24 possible outcomes.

Step-by-step explanation:

1. 1-2-3-4

2. 1-4-3-2

3. 1-4-2-3

4. 1-2-4-3

5. 1-3-2-4

6. 1-4-3-2

7. 2-4-3-1

8. 2-1-3-4

9. 2-1-4-3

10. 2-4-1-3

11. 2-3-1-4

12. 2-3-4-1

13. 3-2-1-4

14. 3-2-4-1

15. 3-1-2-4

16. 3-1-4-2

17. 3-4-1-2

18. 3-4-2-1

19. 4-3-2-1

20. 4-3-1-2

21. 4-2-3-1

22. 4-2-1-3

23. 4-1-2-3

24. 4-1-3-2

Hope this helps!!


5 0
3 years ago
Last year, elsa opened an investment account with 8500 . at the end of the year, the amount in the account had increased by 27.6
Dafna11 [192]
8500 + 27.6 = 8527 dollars and 60 cents
4 0
3 years ago
Other questions:
  • Ronald and shella spent $88 to go to to dinner thirty percent of this cost was for parking downtown that spent the remainder of
    15·1 answer
  • A line has a slope of –3 and a y-intercept of (0, –1). What is the equation of the line that is parallel to the given line and p
    5·1 answer
  • ryan spends 10 1/2 hours at work each day. he has a 3/4 hour lunch and receives two 1/4 hour breaks. how much time does ryan spe
    12·1 answer
  • Evaluate <br> (86)(8-3)(4-2)<br> 2<br> .<br><br> A) 8 <br> B) 16 <br> C) 32 <br> D) 64
    13·1 answer
  • Who knows this please!!!
    13·1 answer
  • After a nutrition experiment is completed, a report describing the project is read, analyzed, and evaluated by two or more resea
    9·1 answer
  • Can someone help me so i can do the rest like this on my own/
    8·1 answer
  • What is the reciprocal of 5 3/7
    9·1 answer
  • I'LL GIVE BRAINLIEST:
    9·2 answers
  • Pls help I’ll brainlest due in 10 Minutes
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!