Octavia simplified the expression as shown. Explain Octavia's error and correct work. (3x^9)^2(3x^2)^4
3^2 × x^11 ×3^4 × x^6
3^2 × 3^4 × x^11 × x^6
3^6 × x^17
729x^17

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) = .