If x 60°+ y 0°+ 30°- 45°= 5, then find the value of x + 2y.

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 21(a)

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, section B, question 21(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(a) · 2 marks · Very short answerIntroduction to Trigonometry

If $x cos 6 0^{\circ} + y cos 0^{\circ} + sin 3 0^{\circ} - cot 4 5^{\circ} = 5$ , then find the value of $x + 2 y$ .

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

Write down the standard values of $cos 6 0^{\circ}$ , $cos 0^{\circ}$ , $sin 3 0^{\circ}$ and $cot 4 5^{\circ}$ .

Hint 2

After substituting, multiply the whole equation by 2.

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 $cos 6 0^{\circ} = \frac{1}{2}$ , $cos 0^{\circ} = 1$ , $sin 3 0^{\circ} = \frac{1}{2}$ and $cot 4 5^{\circ} = 1$ :
$x (\frac{1}{2}) + y (1) + \frac{1}{2} - 1 = 5$
1½ marks
$\frac{x}{2} + y = \frac{11}{2}$ . Multiplying by 2: $x + 2 y = 11$ .
½ mark

Answer: $x + 2 y = 11$

Where the marks are

Substitutes the correct values of all four trigonometric ratios ( $1 \frac{1}{2}$ marks)
Simplifies to $x + 2 y = 11$ ( $\frac{1}{2}$ mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)

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 21(a)

Hints

Step-by-step solution

Revise the chapter

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