ICSE Class 10

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.

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Sample questions

  1. 1.Which of the following correctly proves the identity $\tan^2 A \sec^2 B - \sec^2 A \tan^2 B = \tan^2 A - \tan^2 B$?
    • A.Substitute $\sec^2 B = 1 + \tan^2 B$ and $\sec^2 A = 1 + \tan^2 A$ into the LHS and simplify to match the RHS.
    • B.Factor out $\tan^2 A \tan^2 B$ from the LHS and simplify using $\sec^2 A = 1 + \tan^2 A$.
    • C.Rewrite $\tan^2 A$ and $\tan^2 B$ in terms of $\sin$ and $\cos$, then cross-multiply to cancel terms.
    • D.Use $\sec^2 A = \tan^2 A + 1$ only on the first term of the LHS and ignore the second term.
  2. 2.The expression $\frac{\cos^3 \theta + \sin^3 \theta}{\cos \theta + \sin \theta} + \frac{\cos^3 \theta - \sin^3 \theta}{\cos \theta - \sin \theta}$ simplifies to which of the following values?
    • A.1
    • B.2
    • C.$\sin \theta \cos \theta$
    • D.$1 + \sin \theta \cos \theta$
  3. 3.Prove the trigonometric identity by simplifying the left-hand side: $(1 + \cot A - \csc A)(1 + \tan A + \sec A) = ?$
    • A.2
    • B.$\sin A + \cos A$
    • C.$2 \sec A \csc A$
    • D.$1 + \tan A + \cot A$
  4. 4.If $\tan\theta + \sin\theta = m$ and $\tan\theta - \sin\theta = n$, then $m^2 - n^2$ is equal to
    • a.$\sqrt{mn}$
    • b.$\sqrt{\frac{m}{n}}$
    • c.$4\sqrt{mn}$
    • d.None of these
  5. 5.Which of the following correctly proves the identity: $\frac{1}{(1 + \tan^2 A)} + \frac{1}{(1 + \cot^2 A)} = 1$?
    • A.$\frac{1}{1 + \tan^2 A} + \frac{1}{1 + \cot^2 A} = \frac{1}{\sec^2 A} + \frac{1}{\csc^2 A} = \cos^2 A + \sin^2 A = 1$
    • B.$\frac{1}{1 + \tan^2 A} + \frac{1}{1 + \cot^2 A} = \frac{1}{\csc^2 A} + \frac{1}{\sec^2 A} = \sin^2 A + \cos^2 A = 1$
    • C.$\frac{1}{1 + \tan^2 A} + \frac{1}{1 + \cot^2 A} = \tan^2 A + \cot^2 A = \sec^2 A - 1 + \csc^2 A - 1 = 0$
    • D.$\frac{1}{1 + \tan^2 A} + \frac{1}{1 + \cot^2 A} = \frac{1}{\sec^2 A} + \frac{1}{\csc^2 A} = \cos A + \sin A = 1$

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