Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Help please! Calculate the exact value of cos (a-b) given that sin a= 12/13 with pi/2

Help Please Calculate The Exact Value Of Cos Ab Given That Sin A 1213 With Pi2 class=

Sagot :

coolstick

Answer:

56/65

Step-by-step explanation:

First, we know that cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

We know what sin(a) and sin(b) are, and to get cos(a), we can take the equation sin²a + cos²a = 1

Thus,

(12/13)² + cos²a = 1

1 - (12/13)² = cos²a

1- 144/169 = cos²a

cos²a = 25/169

cos(a) = 5/13

Similarly,

(3/5)² + cos²b = 1

1 - (3/5)² = cos²b

1 - 9/25 = cos²b

cos²b = 16/25

cos(b) = 4/5

Our answer is

cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

cos(a-b)  = (5/13)(4/5) + (12/13)(3/5)

cos(a-b)  = 20/65 + 36/65

cos(a-b)  = 56/65

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.