Verify that 2A = (1 - ² A)/(1 + ² A) for A = 30°.

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 22(b)

Set in the CBSE Class 10 board exam of 2025, paper 430/5/1, section B, question 22(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(b) · 2 marks · Very short answerIntroduction to Trigonometry

Verify that $cos 2 A = \frac{1 - t a n ^{2} A}{1 + t a n ^{2} A}$ for $A = 3 0^{\circ}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/5/1.

Hints

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

Hint 1

With $A = 3 0^{\circ}$ , what is $2 A$ ? Find the cosine of that angle.

Hint 2

Use $tan 3 0^{\circ} = \frac{1}{3}$ , so $tan^{2} 3 0^{\circ} = \frac{1}{3}$ , and simplify the fraction.

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.

LHS $= cos 2 A = cos 6 0^{\circ} = \frac{1}{2}$
½ mark
RHS $= \frac{1 - t a n ^{2} 3 0 ^{\circ}}{1 + t a n ^{2} 3 0 ^{\circ}} = \frac{1 - \frac{1}{3}}{1 + \frac{1}{3}}$ [since $tan 3 0^{\circ} = \frac{1}{3}$ ]
1 mark
$= \frac{2/3}{4/3} = \frac{1}{2} =$ LHS. Hence verified.
½ mark

Answer: LHS = RHS = $\frac{1}{2}$ ; verified.

Where the marks are

Finds LHS $= cos 6 0^{\circ} = \frac{1}{2}$ (½ mark)
Substitutes $tan^{2} 3 0^{\circ} = \frac{1}{3}$ in RHS (1 mark)
Simplifies RHS to $\frac{1}{2}$ and concludes (½ mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Proving Simple Trigonometric Identities

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 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 22(b)

Hints

Step-by-step solution

Revise the chapter

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