Answer the following. (a) Evaluate: ( 45°)/( 30°+ 60°) (b) Verify that 2A = (2 A)/(1 + ² A), for A = 30°.

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 24(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/6/1, section B, question 24(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(a) · 2 marks · Very short answerIntroduction to Trigonometry

Answer the following.

(a)
Evaluate: $\frac{cos 4 5 ^{\circ}}{tan 3 0 ^{\circ} + sin 6 0 ^{\circ}}$
0 marks
(b)
Verify that $sin 2 A = \frac{2 tan A}{1 + tan ^{2} A}$ , for $A = 3 0^{\circ}$ .
0 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/6/1.

Hints

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

Hint 1

Recall the standard values of cos 45°, tan 30° and sin 60°.

Hint 2

Add the two fractions in the denominator using the common denominator $23$ , then divide.

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

Answer: $\frac{2 3}{5 2} = \frac{6}{5}$

Where the marks are

Substitutes correct values of $cos 4 5^{\circ}, tan 3 0^{\circ}, sin 6 0^{\circ}$ and simplifies the denominator (1½ marks)
Final value $\frac{6}{5}$ (½ mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Relationships Between Trigonometric Ratios

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 430/6/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 24(a)

Hints

Step-by-step solution

Revise the chapter

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