ICSE Class 10 Trigonometric Identities — Mock Test (2027)
Free online mock test for Trigonometric Identities (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.
What to expect: This mock test covers key concepts from the Trigonometric Identities chapter — including application-based and competency-focused questions aligned with how ICSE actually sets the paper.
Tip: Attempt without notes first to identify gaps, then review explanations for any wrong answers. Retake after a few days for best retention.
Sample questions
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1.Which of the following expressions is equivalent to $(1 - \sin \theta + \cos \theta)^2$?
- A.$2(1 + \cos \theta)(1 - \sin \theta)$
- B.$2(1 - \cos \theta)(1 + \sin \theta)$
- C.$(1 + \sin \theta + \cos \theta)^2$
- D.$2(1 - \sin \theta - \cos \theta)$
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2.(iii) Which of the following expressions is equivalent to the given trigonometric identity: $\frac{(\cot A + \tan A - 1)(\sin A + \cos A)}{\sin^3 A + \cos^3 A}$?
- A.$\sin A \cos A$
- B.$\sec A + \csc A$
- C.$\sec A \cdot \csc A$
- D.$\tan A + \cot A$
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3.Assertion: $\sin^2 67^\circ + \cos^2 67^\circ = 1$ Reason: For any value of $\theta, \sin^2\theta + \cos^2\theta = 1$ (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true.
- a.Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b.Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c.Assertion (A) is true but reason (R) is false.
- d.Assertion (A) is false but reason (R) is true.
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4.Given that $\sin \alpha = \frac{\sqrt{3}}{2}$ and $\cos \beta = 0$, then the value of $\beta - \alpha$ is
- a.$0^\circ$
- b.$90^\circ$
- c.$60^\circ$
- d.$30^\circ$
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5.Which of the following correctly proves the identity: $\frac{\sec A}{\sec A + 1} + \frac{\sec A}{\sec A - 1} = 2 \csc^2 A$?
- A.$\frac{\sec A}{\sec A + 1} + \frac{\sec A}{\sec A - 1} = \frac{2 \sec^2 A}{\tan^2 A} = 2 (\cot^2 A + 1) = 2 \csc^2 A$
- B.$\frac{\sec A}{\sec A + 1} + \frac{\sec A}{\sec A - 1} = \frac{2 \sec A}{\sec^2 A - 1} = \frac{2 \sec A}{\tan^2 A} = 2 \csc A$
- C.$\frac{\sec A}{\sec A + 1} + \frac{\sec A}{\sec A - 1} = \frac{2 \sec^2 A}{1 - \tan^2 A} = 2 (1 + \cot^2 A) = 2 \sec^2 A$
- D.$\frac{\sec A}{\sec A + 1} + \frac{\sec A}{\sec A - 1} = \frac{2 \sec A}{\sec A - 1} = \frac{2}{\sin A} = 2 \csc^2 A$
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