The value of ²θ - ((1)/(θ) × θ ) is : (A) 1 (B) 0 (C) -1 (D) 2

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2025: question 5

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, section A, question 5, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q5 · 1 mark · MCQIntroduction to Trigonometry

The value of $tan^{2} θ - (\frac{1}{c o s θ} \times sec θ)$ is :

(A)1
(B)0
(C) $- 1$
(D)2

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

What is $\frac{1}{c o s θ}$ equal to?

Hint 2

Use the identity $1 + tan^{2} θ = sec^{2} θ$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Since $\frac{1}{cos θ} = sec θ$ , the bracket equals $sec θ \times sec θ = sec^{2} θ$ .
So the expression is $tan^{2} θ - sec^{2} θ = - (sec^{2} θ - tan^{2} θ) = - 1$ , using $sec^{2} θ - tan^{2} θ = 1$ . This is option (C).
1 mark

Answer: −1, option (C)

Where the marks are

Writes the bracket as $sec^{2} θ$ and uses $sec^{2} θ - tan^{2} θ = 1$ to get $- 1$ , option (C) (1 mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Proving Simple Trigonometric Identities

Practise this chapterBoard-style questions from Introduction to Trigonometry, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 5

Hints

Step-by-step solution

Revise the chapter

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