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.

Sample questions

1. 1.Which of the following simplifies to $\tan A$?
   • A.$\frac{\sin A - 2 \sin^3 A}{2 \cos^3 A - \cos A}$
   • B.$\frac{\sin A + 2 \sin^3 A}{2 \cos^3 A - \cos A}$
   • C.$\frac{2 \sin^3 A - \sin A}{\cos A - 2 \cos^3 A}$
   • D.$\frac{\sin A - 2 \sin^3 A}{\cos A - 2 \cos^3 A}$
2. 2.Prove the following trigonometric identity by selecting the correct simplified form of the left-hand side (L.H.S.): $(\operatorname{cosec}A - \sin A)(\sec A - \cos A)(\tan A + \cot A) = ?$
   • A.$\frac{\cos^2 A \sin^2 A}{\sin A \cos A} \times \frac{1}{\sin A \cos A} = 1$
   • B.$\frac{1 - \sin^2 A}{\sin A} \times \frac{1 - \cos^2 A}{\cos A} \times (\tan A + \cot A) = 1$
   • C.$(\cot A)(\tan A)(1) = 1$
   • D.$\frac{\cos A}{\sin A} + \frac{\sin A}{\cos A} = 1$
3. 3.(iii) Using tables find the value of: $\tan 31^\circ 27'$
   • A.0.6084
   • B.0.6104
   • C.0.6116
   • D.0.6146
4. 4.Which of the following correctly completes the proof that $(\sin A + \cos A)(\sec A + \csc A) = 2 + \sec A \csc A$?
   • A.$(\sin A + \cos A)(\sec A + \csc A) = \tan A + \cot A + 2$
   • B.$(\sin A + \cos A)(\sec A + \csc A) = \sin A \cos A + \sec A \csc A$
   • C.$(\sin A + \cos A)(\sec A + \csc A) = 1 + \sec A + \csc A$
   • D.$(\sin A + \cos A)(\sec A + \csc A) = 2 \tan A + 2 \cot A$
5. 5.Eliminate θ from the following equations: $a \cot \theta + b \csc \theta = x$ and $a \csc \theta + b \cot \theta = y$. Which of the following relations is obtained?
   • A.$b^2 - a^2 = x^2 - y^2$
   • B.$a^2 - b^2 = x^2 - y^2$
   • C.$a^2 + b^2 = x^2 + y^2$
   • D.$x^2 - y^2 = 2ab$