If A=60° and B=30°, verify that: (A+B)= A B+ A B

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 23(B)

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, section B, question 23(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(B) · 2 marks · Very short answerIntroduction to Trigonometry

If $A = 6 0^{\circ}$ and $B = 3 0^{\circ}$ , verify that: $sin (A + B) = sin A cos B + cos A sin B$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/1/1.

Hints

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

Hint 1

Evaluate each side separately.

Hint 2

Use $sin 6 0^{\circ} = cos 3 0^{\circ} = \frac{3}{2}$ and $cos 6 0^{\circ} = sin 3 0^{\circ} = \frac{1}{2}$ .

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 $= sin (6 0^{\circ} + 3 0^{\circ}) = sin 9 0^{\circ} = 1$
1 mark
RHS $= sin 6 0^{\circ} cos 3 0^{\circ} + cos 6 0^{\circ} sin 3 0^{\circ} = \frac{3}{2} \cdot \frac{3}{2} + \frac{1}{2} \cdot \frac{1}{2} = \frac{3}{4} + \frac{1}{4} = 1$ . Hence LHS = RHS, which is verified.
1 mark

Answer: LHS = RHS = 1, verified

Where the marks are

Evaluates LHS $= sin 9 0^{\circ} = 1$ (1 mark)
Evaluates RHS $= \frac{3}{4} + \frac{1}{4} = 1$ and concludes LHS = RHS (1 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 paper2024 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 23(B)

Hints

Step-by-step solution

Revise the chapter

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