If (A + B) = √(3) and (A - B) = (1)/(√(3)); 0° B, find A and B.

MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 24(a)

From the official CBSE sample question paper for 2023-24, 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

If $tan (A + B) = 3$ and $tan (A - B) = \frac{1}{3}$ ; $0^{\circ} < A + B < 9 0^{\circ}$ ; $A > B$ , find A and B.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Which standard angles have tangent $3$ and $\frac{1}{3}$ ?

Hint 2

You get two linear equations in A and B. Add and subtract them.

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.

$tan (A + B) = 3 = tan 6 0^{\circ}$ , so $A + B = 6 0^{\circ}$ …(1)
½ mark
$tan (A - B) = \frac{1}{3} = tan 3 0^{\circ}$ , so $A - B = 3 0^{\circ}$ …(2)
½ mark
Adding (1) and (2): $2 A = 9 0^{\circ}$ , so $A = 4 5^{\circ}$ .
½ mark
Subtracting (2) from (1): $2 B = 3 0^{\circ}$ , so $B = 1 5^{\circ}$ .
½ mark

Answer: $A = 4 5^{\circ}$ , $B = 1 5^{\circ}$

Where the marks are

Gets $A + B = 6 0^{\circ}$ (½ mark)
Gets $A - B = 3 0^{\circ}$ (½ mark)
Finds $A = 4 5^{\circ}$ (½ mark)
Finds $B = 1 5^{\circ}$ (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 paperSample paper 2023-24 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2023-24: question 24(a)

Hints

Step-by-step solution

Revise the chapter

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