If θ + θ = x, then θ - θ will be (A) x (B) x² (C) 2/x (D) 1/x

MathsCBSE Class 10 · Standard · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2025-26: question 5

From the official CBSE sample question paper for 2025-26, 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

If $sec θ + tan θ = x$ , then $sec θ - tan θ$ will be

(A) $x$
(B) $x^{2}$
(C) $\frac{2}{x}$
(D) $\frac{1}{x}$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Recall the identity that links $sec^{2} θ$ and $tan^{2} θ$ .

Hint 2

Factorise $sec^{2} θ - tan^{2} θ$ as a difference of squares.

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.

Use the identity $sec^{2} θ - tan^{2} θ = 1$ , which factorises as $(sec θ + tan θ) (sec θ - tan θ) = 1$ .
So $x (sec θ - tan θ) = 1$ , giving $sec θ - tan θ = \frac{1}{x}$ . The answer is option (D).
1 mark

Answer: 1/x, option (D)

Where the marks are

Uses $sec^{2} θ - tan^{2} θ = 1$ to get $\frac{1}{x}$ , option (D) (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 paperSample paper 2025-26 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2025-26: question 5

Hints

Step-by-step solution

Revise the chapter

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