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.Prove the following trigonometric identity by selecting the correct simplified form of the left-hand side (L.H.S.): $\left(\tan A + \frac{1}{\cos A}\right)^2 + \left(\tan A - \frac{1}{\cos A}\right)^2 = ?$
   • A.$2 \left(\frac{1 + \sin^2 A}{1 - \sin^2 A}\right)$
   • B.$2 \left(\frac{1 + \sin A}{1 - \sin A}\right)$
   • C.$2(\tan^2 A + \sec^2 A)$
   • D.$\frac{2 \sin^2 A}{\cos^2 A}$
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.Simplify: $\frac{\csc^2 67^\circ - \cot^2 67^\circ}{\sec^2 20^\circ - \tan^2 20^\circ}$. What is the value of the simplified expression?
   • A.0
   • B.1
   • C.2
   • D.1/2
4. 4.If $m = a \sec A + b \tan A$ and $n = a \tan A + b \sec A$, then which of the following correctly expresses the value of $m^2 - n^2$?
   • A.$m^2 - n^2 = a^2 - b^2$
   • B.$m^2 - n^2 = (a^2 + b^2)(\sec^2 A - \tan^2 A)$
   • C.$m^2 - n^2 = a^2 + b^2$
   • D.$m^2 - n^2 = (a + b)^2 - (a - b)^2$
5. 5.If $\cos 9\alpha = \sin \alpha$ and $9\alpha < 90^\circ$, then the value of $\tan 5\alpha$ is
   • a.$\frac{1}{\sqrt{3}}$
   • b.$\sqrt{3}$
   • c.1
   • d.0