| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2019 |
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| Session | March |
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| Topic | Implicit equations and differentiation |
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5 The variables \(x\) and \(y\) satisfy the relation \(\sin y = \tan x\), where \(- \frac { 1 } { 2 } \pi < y < \frac { 1 } { 2 } \pi\). Show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { \cos x \sqrt { } ( \cos 2 x ) } .$$