 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/2/b/solution

x

cosh x > 0

and

1 - tanh^{2} x = sech^{2} x

. Hence

cosh x = 1/ 1 - u^{2}

, and multiplying it by

tanh x = u

gives

sinh x = \frac{u}{1 - u ^{2}}, - 1 < u < 1 .

The sign of the numerator preserves the sign of

sinh x

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