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

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 22(b)

Set in the CBSE Class 10 board exam of 2023, 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

For $A = 3 0^{\circ}$ and $B = 6 0^{\circ}$ , 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 2023 board paper, set 430/5/1.

Hints

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

Hint 1

Find A + B first and evaluate the LHS.

Hint 2

For the RHS, substitute $sin 3 0^{\circ}, cos 6 0^{\circ}, cos 3 0^{\circ}, sin 6 0^{\circ}$ from the table.

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 $= sin (3 0^{\circ} + 6 0^{\circ}) = sin 9 0^{\circ} = 1$
½ mark
RHS $= sin 3 0^{\circ} cos 6 0^{\circ} + cos 3 0^{\circ} sin 6 0^{\circ} = \frac{1}{2} \times \frac{1}{2} + \frac{3}{2} \times \frac{3}{2}$
1 mark
$= \frac{1}{4} + \frac{3}{4} = 1$ . Hence LHS = RHS, verified.
½ mark

Answer: LHS = RHS = 1, hence verified

Where the marks are

LHS $= sin 9 0^{\circ} = 1$ (½ mark)
Correct substitution in RHS (1 mark)
RHS = 1, so LHS = RHS (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 paper2023 board paper, set 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 22(b)

Hints

Step-by-step solution

Revise the chapter

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