Find the magnitude and direction of r + a - u

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) = .

Which of these angles are complementary? a. 45o and 45o b. 63o and 117o c. 45o and 135o d. 90o and 45o

Bc and bd are opposite rays. all of the following are true except a)a,b,c,d are collinear b)a,b,c,d are coplanar c)bc=bd d)b is between c and d