Evaluate : (2 30°· 60°· 45°)/(1 - ² 60°)

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 22

Set in the CBSE Class 10 board exam of 2024, paper 30/5/1, section B, question 22, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22 · 2 marks · Very short answerIntroduction to Trigonometry

Evaluate : $\frac{2 t a n 3 0 ^{\circ} \cdot s e c 6 0 ^{\circ} \cdot t a n 4 5 ^{\circ}}{1 - s i n ^{2} 6 0 ^{\circ}}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/5/1.

Hints

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

Hint 1

Recall the standard values of tan 30°, sec 60°, tan 45° and sin 60°.

Hint 2

Simplify the denominator $1 - sin^{2} 6 0^{\circ}$ first, then divide.

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.

Substitute $tan 3 0^{\circ} = \frac{1}{3}$ , $sec 6 0^{\circ} = 2$ , $tan 4 5^{\circ} = 1$ , $sin 6 0^{\circ} = \frac{3}{2}$ :
$\frac{2 \times \frac{1}{3} \times 2 \times 1}{1 - \frac{3}{4}} = \frac{\frac{4}{3}}{\frac{1}{4}}$
1½ marks
$= \frac{16}{3} = \frac{16 3}{3}$
½ mark

Answer: $\frac{16}{3}$ or $\frac{16 3}{3}$

Where the marks are

Correct substitution of all trigonometric values (1½ marks)
Correct simplification to $16/ 3$ (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 paper2024 board paper, set 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 22

Hints

Step-by-step solution

Revise the chapter

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