Evaluate: 4³ 60°+ cosec 30°² 30°

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 21(b)

Set in the CBSE Class 10 board exam of 2026, paper 430/5/1, section B, question 21(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

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

Evaluate: $\frac{4 cos ^{3} 6 0 ^{\circ} + cosec 3 0 ^{\circ}}{tan ^{2} 3 0 ^{\circ}}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/5/1.

Hints

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

Hint 1

Write down $cos 6 0^{\circ}$ , $cosec 3 0^{\circ}$ and $tan 3 0^{\circ}$ from the trigonometric table.

Hint 2

Simplify the numerator and denominator separately before dividing.

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.

Put $cos 6 0^{\circ} = \frac{1}{2}$ , $cosec 3 0^{\circ} = 2$ , $tan 3 0^{\circ} = \frac{1}{3}$ :
$\frac{4 ( \frac{1}{2} ) ^{3} + 2}{( \frac{1}{3} ) ^{2}} = \frac{\frac{1}{2} + 2}{\frac{1}{3}}$
1½ marks
$= \frac{5}{2} \times 3 = \frac{15}{2}$
½ mark

Answer: $\frac{15}{2}$

Where the marks are

Correct substitution of all three standard values (1½ marks)
Simplifies to $\frac{15}{2}$ (½ 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 paper2026 board paper, set 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 21(b)

Hints

Step-by-step solution

Revise the chapter

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