CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 12

Mathematics Objective Questions and Answers: Chapter 08 Introduction to Trigonometry

Access targeted multiple-choice questions for Chapter 08 Introduction to Trigonometry designed to align with the latest CBSE academic syllabus for Class 10 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Download Chapter 08 Introduction to Trigonometry MCQs with Answers

Navigate directly to the 50 objective questions for Chapter 08 Introduction to Trigonometry using the digital viewer below. Each practice set includes verified answer keys, allowing students to instantly cross-check their work and identify areas requiring further revision.

Multiple Choice Questions

Question: If \(\sec\theta - \tan\theta = m\), then the value of \(\sec\theta + \tan\theta\) is
(a) \(1 - \frac{1}{m}\)
(b) \(m^2 - 1\)
(c) \(\frac{1}{m}\)
(d) \(-m\)
Show Answer & Explanation

Answer: (c) \(\frac{1}{m}\)

Explanation:
1. \((\sec\theta - \tan\theta)(\sec\theta + \tan\theta) = \sec^2\theta - \tan^2\theta = 1\).
2. So \(\sec\theta + \tan\theta = \frac{1}{m}\).

Question: If \(\theta\) is an acute angle of a right angled triangle, which of the following equations is not true?
(a) \(\sin\theta \cot\theta = \cos\theta\)
(b) \(\cos\theta \tan\theta = \sin\theta\)
(c) \(\csc^2\theta - \cot^2\theta = 1\)
(d) \(\tan^2\theta - \sec^2\theta = 1\)
Show Answer & Explanation

Answer: (d) \(\tan^2\theta - \sec^2\theta = 1\)

Explanation:
1. \(\sec^2\theta - \tan^2\theta = 1\), so \(\tan^2\theta - \sec^2\theta = -1\), not \(1\).
2. The other three are true.

Question: The simplified form of \(\frac{\cos^2\theta - 1}{\sin^2\theta}\) is
(a) \(\tan^2\theta\)
(b) \(\sec^2\theta\)
(c) 1
(d) -1
Show Answer & Explanation

Answer: (d) -1

Explanation:
1. \(\cos^2\theta - 1 = -\sin^2\theta\), so the expression is \(-1\).

Question: If \(\sin\theta - \cos\theta = 0\), then the value of \(\sin^4\theta + \cos^4\theta\) is
(a) 1
(b) \(\frac{3}{4}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{1}{4}\)
Show Answer & Explanation

Answer: (c) \(\frac{1}{2}\)

Explanation:
1. \(\sin\theta = \cos\theta\) gives \(\theta = 45^\circ\).
2. \(\sin^4 45^\circ + \cos^4 45^\circ = \frac{1}{4} + \frac{1}{4} = \frac{1}{2}\).

Question: If \(\sin\theta = \frac{a}{b}\), then \(\cos\theta\) is equal to
(a) \(\frac{b}{\sqrt{b^2 - a^2}}\)
(b) \(\frac{b}{a}\)
(c) \(\frac{\sqrt{b^2 - a^2}}{b}\)
(d) \(\frac{a}{\sqrt{b^2 - a^2}}\)
Show Answer & Explanation

Answer: (c) \(\frac{\sqrt{b^2 - a^2}}{b}\)

Explanation:
1. Base \(= \sqrt{b^2 - a^2}\), so \(\cos\theta = \frac{\sqrt{b^2 - a^2}}{b}\).

Teacher's Note:
1. The square roots in options (a) and (d) are reconstructed from the source's layout.

Question: If \(\cos(a + b) = 0\), then \(\sin(a - b)\) can be reduced to
(a) \(\cos b\)
(b) \(\cos 2b\)
(c) \(\sin a\)
(d) \(\sin 2a\)
Show Answer & Explanation

Answer: (b) \(\cos 2b\)

Explanation:
1. \(\cos(a + b) = 0\) gives \(a + b = 90^\circ\), so \(a = 90^\circ - b\).
2. \(\sin(a - b) = \sin(90^\circ - 2b) = \cos 2b\).

Question: If \(\cos 9a = \sin a\) and \(9a < 90^\circ\), then the value of \(\tan 5a\) is
(a) \(\frac{1}{\sqrt{3}}\)
(b) \(\sqrt{3}\)
(c) 1
(d) 0
Show Answer & Explanation

Answer: (c) 1

Explanation:
1. \(\cos 9a = \sin(90^\circ - 9a) = \sin a\), so \(90^\circ - 9a = a\), giving \(a = 9^\circ\).
2. \(\tan 5a = \tan 45^\circ = 1\).

Teacher's Note:
1. Option (a) and (b) square roots are reconstructed from the extraction.

Question: If \(\triangle ABC\) is right angled at \(C\), then the value of \(\cos(A + B)\) is
(a) 0
(b) 1
(c) \(\frac{1}{2}\)
(d) \(\frac{\sqrt{3}}{2}\)
Show Answer & Explanation

Answer: (a) 0

Explanation:
1. \(\angle A + \angle B + 90^\circ = 180^\circ\), so \(A + B = 90^\circ\).
2. \(\cos 90^\circ = 0\).

Teacher's Note:
1. Options (c) and (d) are reconstructed from the extraction. Please check against the printed book.

Question: If \(\sin\alpha = \frac{1}{2}\) and \(\cos\beta = \frac{1}{2}\), then the value of \((\alpha + \beta)\) is
(a) \(0^\circ\)
(b) \(30^\circ\)
(c) \(60^\circ\)
(d) \(90^\circ\)
Show Answer & Explanation

Answer: (d) \(90^\circ\)

Explanation:
1. \(\alpha = 30^\circ\) and \(\beta = 60^\circ\), so \(\alpha + \beta = 90^\circ\).

Question: If \(4\tan\theta = 3\), then \(\frac{4\sin\theta - \cos\theta}{4\sin\theta + \cos\theta}\) is equal to
(a) \(\frac{2}{3}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{3}{4}\)
Show Answer & Explanation

Answer: (c) \(\frac{1}{2}\)

Explanation:
1. Divide numerator and denominator by \(\cos\theta\): \(\frac{4\tan\theta - 1}{4\tan\theta + 1} = \frac{3 - 1}{3 + 1} = \frac{1}{2}\).

Question:
Assertion (A): The value of \(\sec^2 10^\circ - \cot^2 80^\circ\) is 1.
Reason (R): The value of \(\sin 30^\circ = \frac{1}{2}\).
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. \(\cot 80^\circ = \tan 10^\circ\), so \(\sec^2 10^\circ - \tan^2 10^\circ = 1\). The assertion is true.
2. \(\sin 30^\circ = \frac{1}{2}\) is true, but it does not explain the assertion.

Question:
Assertion (A): The value of \(\sin\theta = \frac{4}{3}\) is not possible.
Reason (R): Hypotenuse is the largest side in any right angled triangle.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. \(\sin\theta = \frac{P}{H}\) cannot exceed 1, so \(\frac{4}{3}\) is impossible.
2. The reason, that the hypotenuse is the largest side, explains why.

Question:
Assertion (A): \(\sin^2 67^\circ + \cos^2 67^\circ = 1\).
Reason (R): For any value of \(\theta\), \(\sin^2\theta + \cos^2\theta = 1\).
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Substituting \(\theta = 67^\circ\) in the identity gives the assertion. The reason is the identity itself.

Question:
Assertion (A): For \(0 < \theta \le 90^\circ\), \(\csc\theta - \cot\theta\) and \(\csc\theta + \cot\theta\) are reciprocals of each other.
Reason (R): \(\csc^2\theta - \cot^2\theta = 1\).
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. \((\csc\theta + \cot\theta)(\csc\theta - \cot\theta) = 1\), so the two are reciprocals.
2. The identity used in the assertion is the reason.

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Class 10 Mathematics Chapter 08 Introduction to Trigonometry Objective Test Questions

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FAQs

Where can I access latest CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 12?

You can get most exhaustive CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 12 for free on StudiesToday.com. These MCQs for Class 10 Mathematics are updated for the 2026-27 academic session as per CBSE examination standards.

Are Assertion-Reasoning and Case-Study MCQs included in the Mathematics Class 10 material?

Yes, our CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 12 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

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