If θ = (√(3))/(2) and φ = 1/2, then (θ + φ) is: (A) √(3) (B) (1)/(√(3)) (C) 1 (D) not defined

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 8

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section A, question 8, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q8 · 1 mark · MCQIntroduction to Trigonometry

If $cos θ = \frac{3}{2}$ and $sin ϕ = \frac{1}{2}$ , then $tan (θ + ϕ)$ is:

(A) $3$
(B) $\frac{1}{3}$
(C)1
(D)not defined

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

Recognise the standard angles from the given values.

Hint 2

Add the two angles before taking tan.

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.

$cos θ = \frac{3}{2}$ gives $θ = 3 0^{\circ}$ , and $sin ϕ = \frac{1}{2}$ gives $ϕ = 3 0^{\circ}$ .
$tan (θ + ϕ) = tan 6 0^{\circ} = 3$ , which is option (A).
1 mark

Answer: $3$ , option (A)

Where the marks are

Identifies both angles as $3 0^{\circ}$ and evaluates $tan 6 0^{\circ} = 3$ , option (A) (1 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 paper2024 board paper, set 30/3/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2024: question 8

Hints

Step-by-step solution

Revise the chapter

More questions from Introduction to Trigonometry