Use the quadratic formula to determine the exact solutions to the equation. 2x2−5x+1=0

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) = .

From the beginning of the day the temperature rose 15 degrees so that by 4 pm it was 87 degrees. what was the temperature at the start of the day

Find cot x if sin x cot x csc x = √2