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
DochEvi [55]
3 years ago
7

6) If sec theta+tan theta = P. PT sin theta=P^2-1/P^2+1 ...?

Mathematics
1 answer:
jarptica [38.1K]3 years ago
4 0
I will use the letter x instead of theta.

Then the problem is, given sec(x) + tan(x) = P, show that

sin(x) = [P^2 - 1] / [P^2 + 1]

I am going to take a non regular path.

First, develop a little the left side of the first equation:

sec(x) + tan(x) = 1 / cos(x) +  sin(x) / cos(x) = [1 + sin(x)] / cos(x)

and that is equal to P.

Second, develop the rigth side of the second equation:

[p^2 - 1] / [p^2 + 1] =

= [ { [1 + sin(x)] / cos(x) }^2 - 1] / [ { [1 + sin(x)] / cos(x)}^2 +1 ] =

=  { [1 + sin(x)]^2 - [cos(x)]^2 } / { [1 + sin(x)]^2 + [cos(x)]^2 } =

= {1 + 2sin(x) + [sin(x)^2] - [cos(x)^2] } / {1 + 2sin(x) + [sin(x)^2] + [cos(x)^2] }

= {2sin(x) + [sin(x)]^2 + [sin(x)]^2 } / { 1 + 2 sin(x) + 1} =

= {2sin(x) + 2 [sin(x)]^2 } / {2 + 2sin(x)} = {2sin(x) ( 1 + sin(x)} / {2(1+sin(x)} =

= sin(x)

Then, working with the first equation, we have proved that [p^2 - 1] / [p^2 + 1] = sin(x), the second equation.


You might be interested in
Plz help due tomorrow
sp2606 [1]

Answer:

21y^2+11.2

Step-by-step explanation:

4-3y(-7y)+7.2

combine like terms

-3y (-7y) = 21y^2

add 4 to 7.2

11.2

21y^2 + 11.2

8 0
3 years ago
PLZ HELP ME WILL GIVE BRAINLIEST
geniusboy [140]

Answer:

negative slope

Step-by-step explanation:

using the slope equation you can see that the slope is -53

3 0
4 years ago
Figure out the number of solution 6x^2=-2x-2
kifflom [539]
 Choice B is the answer
6 0
3 years ago
Help what is eqation for this.
ICE Princess25 [194]

Answer:

y=-x+10

Step-by-step explanation:

The formula is y=mx+b, where m is the slope and b is the y-intercept. To solve plugin the values for the corresponding variables. It has a slope of -1 and a y-intercept of 10.

4 0
3 years ago
Read 2 more answers
Matt starts swimming lessons on 5 day . He goes every 10 days . How many lessons will Matt go to in 30 days?
Mnenie [13.5K]

Answer: 3 lessons

Step-by-step explanation:

Matt starts swimming lessons on Day 5.

He then goes to swimming lessons every 10 days. The dates he went on lessons are therefore:

First lesson = Day 5

Second lesson = Day 5 + 10 days = Day 15

Third lesson = Day 15 + 10 days = Day 25

Fourth lesson = Day 25 + 10 days= Day 35

<em>He therefore only went for 3 lessons because the 4th lesson was after Day 30. </em>

7 0
3 years ago
Other questions:
  • If 3 x (2 + 3) = •, which expression is equal to •?
    15·1 answer
  • Enter an equation and an answer to the following question:
    14·2 answers
  • What is the LCM of 400 and 900?Step by step
    8·1 answer
  • What is the square root of 456?
    6·2 answers
  • Use I = PRT to find the total amount in the savings account.
    13·2 answers
  • 10 The value of y varies directly with x. If x = 3, then y = 21. What is the value of x when
    10·1 answer
  • Need help with this asap!
    15·1 answer
  • En la papelería " Office Depot", una caja con 24 plumones cuesta $120 y en la papelería "Dabo" una caja con 18 plumones cuesta $
    12·1 answer
  • Please do this I’m lazy and not good at math
    10·1 answer
  • A) side angle side<br> b) side side side <br> c) angle side angle<br> d) not congruent
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!