If θ-θ=m, then the value of θ+θ is: (A) 1-1/m (B) m²-1 (C) 1/m (D) -m

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 7

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, section A, question 7, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q7 · 1 mark · MCQIntroduction to Trigonometry

If $sec θ - tan θ = m$ , then the value of $sec θ + tan θ$ is:

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

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/1/1.

Hints

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

Hint 1

Think of an identity involving $sec^{2} θ$ 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 $sec^{2} θ - tan^{2} θ = 1$ , that is, $(sec θ - tan θ) (sec θ + tan θ) = 1$ .
So $m (sec θ + tan θ) = 1$ , which gives $sec θ + tan θ = \frac{1}{m}$ . The answer is option (C).
1 mark

Answer: $\frac{1}{m}$ , option (C)

Where the marks are

Factorises $sec^{2} θ - tan^{2} θ = 1$ to get $\frac{1}{m}$ , 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 paper2024 board paper, set 30/1/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2024: question 7

Hints

Step-by-step solution

Revise the chapter

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