thuranirajulius54
Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Given that 2 sec?0 – tan²0 = p. show that cosec²theta= p-1/p-2,p≠2

​

Sagot :

jcherry99

Answer:

Step-by-step explanation:

2/cos^2(theta) - sin^2(theta)/cos^(theta) = p

(2 - sin^2(theta) ) / cos^2(theta) = p

cos^2(theta) = 1 - sin^2(theta)                    Relationship between sines and cosines

2 - sin^2(theta)/ (1 - sin^2(theta) ) = p        Everything is now in terms of sines

sin^2 (theta) = 1 / csc ^2 (theta)                 sin^(theta) = 1/csc(theta)

2 - 1/csc^2(theta)                                        Make Left over csc(theta)

==============        =  p

1 - 1/csc^2(theta)

2 csc^2(theta) - 1

------------------------

csc^2(theta)

================    = p         Cancel out denominators (csc^2(theta))

csc(theta)  - 1

-------------------

csc^2(theta)

2 csc^2 (theta) - 1

===============      = p              Multiply both sides by csc^2(theta) - 1

csc^2(theta) - 1

2csc^2(theta) - 1 = p*csc^2(theta) - p   Collect csc^2(theta) on the left, p on the right.

csc^2(theta) (2 - p)  = 1 - p

csc^2(theta) = (1 - p)/(2 - p)

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.