| Exam Board | CAIE |
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| Module | P1 (Pure Mathematics 1) |
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| Year | 2023 |
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| Session | November |
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| Topic | Trig Proofs |
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7
- Verify the identity \(( 2 x - 1 ) \left( 4 x ^ { 2 } + 2 x - 1 \right) \equiv 8 x ^ { 3 } - 4 x + 1\).
- Prove the identity \(\frac { \tan ^ { 2 } \theta + 1 } { \tan ^ { 2 } \theta - 1 } \equiv \frac { 1 } { 1 - 2 \cos ^ { 2 } \theta }\).
- Using the results of (a) and (b), solve the equation
$$\frac { \tan ^ { 2 } \theta + 1 } { \tan ^ { 2 } \theta - 1 } = 4 \cos \theta$$
for \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\).