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 trigonometric identity by selecting the expression that correctly simplifies the left-hand side to match the right-hand side: $\frac{\tan A}{1 - \cot A} + \frac{\cot A}{1 - \tan A} = \sec A \csc A + 1$. Which of the following represents the correct simplification of the left-hand side?
   • A.$\frac{1 + \sin A \cos A}{\sin A \cos A}$
   • B.$\frac{\sin A + \cos A}{\sin A - \cos A}$
   • C.$\frac{\sin^2 A + \cos^2 A}{\sin A \cos A}$
   • D.$\frac{\sin^3 A + \cos^3 A}{\sin A \cos A (\sin A - \cos A)}$
2. 2.(ii) Using the table, find the value of: $\cos 23^\circ 6'$
3. 3.Which of the following correctly simplifies the expression $\sin A (1 + \tan A) + \cos A (1 + \cot A)$?
   • A.$\sec A + \csc A$
   • B.$\sin A + \cos A$
   • C.$\frac{1 + \sin A + \cos A}{\cos A \sin A}$
   • D.$\tan A + \cot A$
4. 4.If $x = p\sec \theta$ and $y = q\tan \theta$, then
   • a.$x^{2} - y^{2} = p^{2}q^{2}$
   • b.$x^{2}q^{2} - y^{2}p^{2} = pq$
   • c.$x^{2}q^{2} - y^{2}p^{2} = \frac{1}{p^{2}q^{2}}$
   • d.$x^{2}q^{2} - y^{2}p^{2} = p^{2}q^{2}$
5. 5.Prove the trigonometric identity by selecting the correct simplification step: $\sec^2 A + \operatorname{cosec}^2 A = \sec^2 A \operatorname{cosec}^2 A$
   • A.$\frac{1}{\cos^2 A} + \frac{1}{\sin^2 A} = \frac{\sin^2 A + \cos^2 A}{\sin^2 A \cos^2 A} = \frac{1}{\sin^2 A \cos^2 A}$
   • B.$\frac{1}{\cos^2 A} + \frac{1}{\sin^2 A} = \frac{2}{\sin^2 A \cos^2 A}$ (using $\sin^2 A + \cos^2 A = 2$)
   • C.$\sec^2 A + \operatorname{cosec}^2 A = \frac{1}{\cos^2 A + \sin^2 A} = 1$
   • D.$\frac{1}{\cos^2 A} + \frac{1}{\sin^2 A} = \frac{\cos^2 A + \sin^2 A}{\cos^2 A \sin^2 A} = \frac{1}{\cos^2 A \sin^2 A} + 1$