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.Given $x \sin^3 \theta + y \cos^3 \theta = \sin \theta \cos \theta$ and $x \sin \theta = y \cos \theta$, which of the following must be true?
- A.$x^2 - y^2 = 1$
- B.$x^2 + y^2 = 1$
- C.$x + y = 1$
- D.$x y = 1$
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2.If $2\cos \theta = \frac{2}{5}$, find $\sin \theta$ without using tables.
- A.$\frac{2\sqrt{6}}{5}$
- B.$\frac{\sqrt{24}}{5}$
- C.$\frac{2}{5}$
- D.$\frac{\sqrt{6}}{5}$
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3.Which of the following correctly proves the identity: $\csc A (1 + \cos A)(\csc A - \cot A) = 1$?
- A.$(1 + \cos A)(1 - \cos A) = 1 - \cos^2 A = \sin^2 A$, which simplifies to 1 when multiplied by $\csc A$.
- B.$\csc A (1 + \cos A)(\csc A - \cot A) = (1 + \cos A)(\csc^2 A - \csc A \cot A) = 1 + \cos A - \cos A = 1$.
- C.$\csc A (1 + \cos A)(\csc A - \cot A) = (1 + \cos A)(1 - \sin A) = 1 - \sin A + \cos A - \sin A \cos A$.
- D.$\csc A - \cot A = \sin A$, so the expression simplifies to $\csc A (1 + \cos A) \sin A = 1 + \cos A$.
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4.If $\tan A + \sin A = m$ and $\tan A - \sin A = n$, which of the following correctly relates $m$, $n$, and $A$?
- A.$m^2 - n^2 = 4\sqrt{mn}$
- B.$m^2 + n^2 = 4\sqrt{mn}$
- C.$m^2 - n^2 = 4mn$
- D.$m^2 - n^2 = 2\sqrt{mn}$
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5.(i) Using tables, find the value of: $\sin 83^\circ 12'$
- A.0.9930
- B.0.9390
- C.0.9903
- D.0.9929
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