Trigonometry Exam Prep
Full explanation, worked examples & memory tricks in the app
Trigonometry Exam Prep
English 10 leveled MCQs Free
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What you'll study, topic by topic
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Sample questions with model answers
Every question in the paper gets a full exam-length answer in the app — organised by marks, the way a topper writes it.
6 marks Long answer
Prove that $\frac{\tan\theta}{1-\cot\theta} + \frac{\cot\theta}{1-\tan\theta} = 1 + \sec\theta \cosec\theta$
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Use algebraic manipulation and trigonometric identities to prove the equality.
The full exam-length answer is in the app.
6 marks Long answer
Prove that $\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac{1}{\sec\theta - \tan\theta}$
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Apply trigonometric identities to simplify both sides and prove the equality.
The full exam-length answer is in the app.
6 marks Long answer
Prove that $\frac{\tan\theta + \sec\theta - 1}{\tan\theta - \sec\theta + 1} = \frac{1+\sin\theta}{\cos\theta}$
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Use trigonometric identities and algebraic manipulation to show the equality.
The full exam-length answer is in the app.
6 marks Long answer
Prove that $(\sin A + \cosec A)^2 + (\cos A + \sec A)^2 = 7 + \tan^2 A + \cot^2 A$
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Expand both sides and simplify to prove the identity.
The full exam-length answer is in the app.
6 marks Long answer
Prove that $\frac{\cot A - \cos A}{\cot A + \cos A} = \frac{\cosec A - 1}{\cosec A + 1}$
Show answer outline
Use trigonometric identities to simplify both sides and prove the equality.
The full exam-length answer is in the app.
6 marks Long answer
Prove that $\frac{\cos\theta - \sin\theta + 1}{\cos\theta + \sin\theta - 1} = \cosec A + \cot A$
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Manipulate the left-hand side and show it equals the right-hand side.
The full exam-length answer is in the app.
3 marks Medium answer
In $\triangle OPQ$, right-angled at P, OP = 7 cm and OQ - PQ = 1 cm. Determine the values of cos Q and tan Q.
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Use Pythagorean theorem to find PQ and then calculate cos Q and tan Q.
The full exam-length answer is in the app.
3 marks Medium answer
Find the value of trigonometric ratios of $60^\circ$ geometrically.
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Use the properties of equilateral triangles to find the ratios.
The full exam-length answer is in the app.
3 marks Medium answer
If $\cot(A+B) = \sqrt{3}$ and $\cot(A-B) = \frac{1}{\sqrt{3}}$, then find the value of A and B.
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Use cotangent addition formulas to solve for A and B.
The full exam-length answer is in the app.
1 marks Short answer
Evaluate: $ \frac{4(\cos^2 45^\circ + \tan^2 60^\circ) + 6(\sin^2 45^\circ - \tan^2 60^\circ)}{\tan 30^\circ + \cot 60^\circ} $
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Evaluate the expression using trigonometric values.
The full exam-length answer is in the app.
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