Evaluate : ² 60°- 2² 30°- 2² 30°.

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

CBSE Class 10 Mathematics Basic 2023: question 22

Set in the CBSE Class 10 board exam of 2023, paper 430/1/1, 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 : $tan^{2} 6 0^{\circ} - 2 cosec^{2} 3 0^{\circ} - 2 tan^{2} 3 0^{\circ}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/1/1.

Hints

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

Hint 1

Recall the standard trigonometric ratio values for 30° and 60°.

Hint 2

$cosec 3 0^{\circ} = \frac{1}{s i n 3 0 ^{\circ}}$ ; square each value before multiplying by the coefficient.

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.

Using $tan 6 0^{\circ} = 3$ , $cosec 3 0^{\circ} = 2$ , $tan 3 0^{\circ} = \frac{1}{3}$ : the expression $= (3)^{2} - 2 (2)^{2} - 2 (\frac{1}{3})^{2}$ .
1½ marks
$= 3 - 8 - \frac{2}{3} = - \frac{17}{3}$ .
½ mark

Answer: $- \frac{17}{3}$

Where the marks are

Substitutes correct values of $tan 6 0^{\circ}$ , $cosec 3 0^{\circ}$ , $tan 3 0^{\circ}$ (1½ marks)
Simplifies to $- \frac{17}{3}$ (½ 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 paper2023 board paper, set 430/1/1 (Basic): 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 Basic 2023: question 22

Hints

Step-by-step solution

Revise the chapter

More questions from Introduction to Trigonometry