Vardaan Learning Institute
Previous Year Questions: Introduction to Trigonometry
Class: 10 (CBSE)
Subject: Mathematics
Chapter: 08
BOARD EXAM 2025 (Set 30/6/3)
Q3.
If \(x = 2 \sin 60� \cos 60�\) and \(y = \sin^2 30� - \cos^2 30�\) and \(x^2 = ky^2\), the value of \(k\) is
(A) \(\sqrt{3}\)
(B) \(-\sqrt{3}\)
(C) 3
(D) -3
[1 Mark]
Q9.
In a right triangle ABC, right-angled at A, if \(\sin B = \frac{1}{4}\), then the value of \(\sec B\) is
(A) 4
(B) \(\frac{\sqrt{15}}{4}\)
(C) \(\sqrt{15}\)
(D) \(\frac{4}{\sqrt{15}}\)
[1 Mark]
Q21 (a).
If \(a \sec \theta + b \tan \theta = m\) and \(b \sec \theta + a \tan \theta = n\), prove that \(a^2 + n^2 = b^2 + m^2\).
[2 Marks]
OR
Q21 (b).
Use \(\sin^2 A + \cos^2 A = 1\) to prove \(\tan^2 A + 1 = \sec^2 A\). Find \(\tan A\) when \(\sec A = \frac{5}{3}\).
[2 Marks]
Q28 (a).
Prove that: \(\frac{\cos \theta - 2 \cos^3 \theta}{\sin \theta - 2 \sin^3 \theta} + \cot \theta = 0\)
[3 Marks]
OR
Q28 (b).
Given \(\sin \theta + \cos \theta = x\), prove that \(\sin^4 \theta + \cos^4 \theta = \frac{2 - (x^2 - 1)^2}{2}\).
[3 Marks]