If θ = 24/7, then find the value of θ + θ.

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 24(A)

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section B, question 24(A), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(A) · 2 marks · Very short answerIntroduction to Trigonometry

If $tan θ = \frac{24}{7}$ , then find the value of $sin θ + cos θ$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/1/1.

Hints

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

Hint 1

Draw a right triangle in which tan θ is perpendicular over base.

Hint 2

Use Pythagoras theorem to find the hypotenuse from sides 24 and 7.

Hint 3

Then sin θ = perpendicular/hypotenuse and cos θ = base/hypotenuse.

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 $tan θ = \frac{perpendicular}{base} = \frac{24}{7}$ , take a right triangle with perpendicular $= 24 k$ and base $= 7 k$ .
½ mark
By Pythagoras theorem, hypotenuse $= (24 k)^{2} + (7 k)^{2} = 576 k^{2} + 49 k^{2} = 625 k^{2} = 25 k$ .
So $sin θ = \frac{24 k}{25 k} = \frac{24}{25}$ and $cos θ = \frac{7 k}{25 k} = \frac{7}{25}$ .
1 mark
$sin θ + cos θ = \frac{24}{25} + \frac{7}{25} = \frac{31}{25}$
½ mark

Answer: $sin θ + cos θ = \frac{31}{25}$

Where the marks are

Finds the hypotenuse 25 and gets $sin θ = \frac{24}{25}$ and $cos θ = \frac{7}{25}$ (1½ marks)
Adds them correctly to get $\frac{31}{25}$ (½ mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Finding Ratios from a Given Ratio

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 paper2026 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 24(A)

Hints

Step-by-step solution

Revise the chapter

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