If α = 1/2, then find the value of (3α - 4³α).

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 21

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section B, question 21, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21 · 2 marks · Very short answerIntroduction to Trigonometry

If $sin α = \frac{1}{2}$ , then find the value of $(3 cos α - 4 cos^{3} α)$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/4/1.

Hints

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

Hint 1

Which standard angle has sine equal to $\frac{1}{2}$ ?

Hint 2

Use $cos 3 0^{\circ} = \frac{3}{2}$ and cube it carefully: $(3)^{3} = 33$ .

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.

$sin α = \frac{1}{2} = sin 3 0^{\circ} \Rightarrow α = 3 0^{\circ}$
½ mark
$3 cos 3 0^{\circ} - 4 cos^{3} 3 0^{\circ} = 3 (\frac{3}{2}) - 4 (\frac{3}{2})^{3} = \frac{3 3}{2} - \frac{4 \cdot 3 3}{8}$
1 mark
$= \frac{3 3}{2} - \frac{3 3}{2} = 0$
½ mark

Answer: 0

Where the marks are

Identifies $α = 3 0^{\circ}$ (½ mark)
Substitutes $cos 3 0^{\circ} = \frac{3}{2}$ and simplifies the cube correctly (1 mark)
Obtains value 0 (½ mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Trigonometric Ratios of 30°, 45° and 60°

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 paper2023 board paper, set 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 21

Hints

Step-by-step solution

Revise the chapter

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