[3/4² 30°- ² 45°+ ² 60° ] is equal to (A) -1 (B) 5/6 (C) (-3)/(2) (D) 1/6

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 9

Set in the CBSE Class 10 board exam of 2023, paper 30/1/1, section A, question 9, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q9 · 1 mark · MCQIntroduction to Trigonometry

$[\frac{3}{4} tan^{2} 3 0^{\circ} - sec^{2} 4 5^{\circ} + sin^{2} 6 0^{\circ}]$ is equal to

(A)-1
(B) $\frac{5}{6}$
(C) $\frac{- 3}{2}$
(D) $\frac{1}{6}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/1/1.

Hints

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

Hint 1

Recall $tan 3 0^{\circ} = 1/ 3$ , $sec 4 5^{\circ} = 2$ , $sin 6 0^{\circ} = 3 /2$ .

Hint 2

Square each value, then substitute.

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.

Use the standard values: $tan^{2} 3 0^{\circ} = \frac{1}{3}$ , $sec^{2} 4 5^{\circ} = 2$ , $sin^{2} 6 0^{\circ} = \frac{3}{4}$ .
$\frac{3}{4} \cdot \frac{1}{3} - 2 + \frac{3}{4} = \frac{1}{4} - 2 + \frac{3}{4} = 1 - 2 = - 1$ . Option (A).
1 mark

Answer: −1, option (A)

Where the marks are

Substitutes the standard values and simplifies to −1, option (A) (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 paper2023 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 9

Hints

Step-by-step solution

Revise the chapter

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