Evaluate : 30° 60°+ 30° 60°- 45°

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2024: question 25

Set in the CBSE Class 10 board exam of 2024, paper 430/4/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerIntroduction to Trigonometry

Evaluate : $sin 3 0^{\circ} cos 6 0^{\circ} + cos 3 0^{\circ} sin 6 0^{\circ} - cot 4 5^{\circ}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/4/1.

Hints

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

Hint 1

Recall the table of trigonometric ratios for 30°, 45° and 60°.

Hint 2

cot 45° = 1. Multiply each pair of values, then add and subtract.

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.

Substitute the standard values: $sin 3 0^{\circ} = \frac{1}{2}, cos 6 0^{\circ} = \frac{1}{2}, cos 3 0^{\circ} = \frac{3}{2}, sin 6 0^{\circ} = \frac{3}{2}, cot 4 5^{\circ} = 1$ . The expression becomes $\frac{1}{2} \times \frac{1}{2} + \frac{3}{2} \times \frac{3}{2} - 1$ .
1½ marks
$= \frac{1}{4} + \frac{3}{4} - 1 = 0$
½ mark

Answer: 0

Where the marks are

Substitutes all five trigonometric values correctly (1½ marks)
Simplifies to 0 (½ mark)

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 paper2024 board paper, set 430/4/1 (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 2024: question 25

Hints

Step-by-step solution

Revise the chapter

More questions from Introduction to Trigonometry