thuranirajulius54
Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. 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 hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.