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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) = .
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Consider this expression and the steps to evaluate it. 4^5(−2)^9/4^8(−2)^3 1. apply the quotient of powers: (−2)^a/4^b 2. evaluate powers: c/d select the value of each variable. a = _ b = _ c = _ d = _
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