MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 25(B)

From the official CBSE sample question paper for 2025-26, section B, question 25(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(B) · 2 marks · Very short answerIntroduction to Trigonometry

If $sin x = \frac{7}{25}$ , where $x$ is an acute angle, then find the value of $sin x \cdot cos x (tan x + cot x)$ .

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

Write $tan x$ and $cot x$ using $sin x$ and $cos x$ .

Hint 2

After taking the LCM inside the bracket, an identity makes the numerator very simple.

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.

$sin x cos x (tan x + cot x) = sin x cos x (\frac{s i n x}{c o s x} + \frac{c o s x}{s i n x})$
½ mark
$= sin x cos x \cdot \frac{s i n ^{2} x + c o s ^{2} x}{s i n x c o s x} = sin^{2} x + cos^{2} x = 1$ . The value is 1 for every acute $x$ , so with $sin x = \frac{7}{25}$ it is 1. (Check: $cos x = \frac{24}{25}$ , $\frac{7}{25} \cdot \frac{24}{25} (\frac{7}{24} + \frac{24}{7}) = \frac{168}{625} \cdot \frac{625}{168} = 1$ .)
1½ marks

Answer: 1

Where the marks are

Writes $tan x$ and $cot x$ in terms of $sin x$ and $cos x$ (½ mark)
Simplifies using $sin^{2} x + cos^{2} x = 1$ to get 1 (1½ marks)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Trigonometric Ratios of an Acute Angle

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 (Basic): 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 Basic sample paper 2025-26: question 25(B)

Hints

Step-by-step solution

Revise the chapter

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