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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) = .

For f(x) = 3x+1 and g(x) = x2 - 6, find (g/f)(x)

Evaluate the expression for the given value of the variable. | ? 4 b ? 8 | + ? ? ? 1 ? b 2 ? ? + 2 b 3 -4b-8+-1-b2+2b3 ; b = ? 2 b=-2