45. Given: The circles share the same center, O, BP is tangent to the inner circle at N, PA is tangent to the inner circle at M, m 106°
N
Y
O 120°
bo
Р
X
M
106°

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

Select the correct answer. what is the exact value of sin (157.5°)? a. 'sqrt(2 - sqrt(2))/2 b. *"-"'sqrt(2 + sqrt(2))/29 c.'sqrt(2 + sqrt(2))/4" d. "-"sqrt(2 + sqrt(2))/4)

Edith is shopping for a new leather couch. jordan’s furniture has one that costs $3,000. however, this weekend she can get a 15% discount. how much money will edith save if she buys the couch this weekend? a $15b $2,550c $45,000d $450