Download and practise with this A-Level Pure Mathematics 2022 question paper. Useful for revision, practice, and exam preparation in Zimbabwe.
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This is the A-Level Pure Mathematics question paper from 2022. Use it for exam practice under timed conditions. Time allowed: 1 hour.
A' LEVEL
PURE MATHEMATICS
TRIGONOMETRY TEST 9
TIME: 1 hour
45 marks
Answer all questions.
[If a numerical answer cannot be given exactly, and the accuracy required is not specified in the question, then in the case of an angle it should be given correct to the nearest degree, and in other cases it should be given to 2 significant figures.]
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Sharewell B. C
1. Prove the following identities,
a) $\frac{1-2 \cos ^{2} x}{\cos x \sin x} \equiv \tan x-\cot x$
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b) $\sqrt{\frac{1+\sin x}{1-\sin x}} \equiv \sec x+\tan x$
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c) $\frac{\left(2 \cos ^{2} x-1\right)^{2}}{\cos ^{4} x-\sin ^{4} x} \equiv 1-2 \sin ^{2} x$
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d) $\frac{1+\tan ^{2} x}{1+\cot ^{2} x} \equiv \sec ^{2} x-1$
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e) $2 \cos x-\frac{2 \cos x}{1-\tan x} \equiv \frac{-\sin 2 x}{\sin x-\cos x}$
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