| Exam Board | Edexcel |
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| Module | F3 (Further Pure Mathematics 3) |
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| Year | 2022 |
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| Session | June |
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| Topic | Hyperbolic functions |
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4.
$$y = \operatorname { artanh } \left( \frac { \cos x + a } { \cos x - a } \right)$$
where \(a\) is a non-zero constant.
Show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = k \tan x$$
where \(k\) is a constant to be determined.