Evaluate: (2² 60°- ² 30°)/(² 45°)

MathsCBSE Class 10 · Standard · Sample paper, session 2024-25 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard sample paper 2024-25: question 23

From the official CBSE sample question paper for 2024-25, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerIntroduction to Trigonometry

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

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Write down the standard values of $sin 6 0^{\circ}$ , $tan 3 0^{\circ}$ and $sec 4 5^{\circ}$ .

Hint 2

Square each value first, then simplify the numerator before dividing by the denominator.

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.

Standard values: $sin 6 0^{\circ} = \frac{3}{2}$ , $tan 3 0^{\circ} = \frac{1}{3}$ , $sec 4 5^{\circ} = 2$ .
Substituting: $\frac{2 ( \frac{3}{2} ) ^{2} - ( \frac{1}{3} ) ^{2}}{( 2 ) ^{2}} = \frac{2 \cdot \frac{3}{4} - \frac{1}{3}}{2} = \frac{\frac{3}{2} - \frac{1}{3}}{2}$
1½ marks
$= \frac{\frac{9 - 2}{6}}{2} = \frac{7}{6} \times \frac{1}{2} = \frac{7}{12}$
½ mark

Answer: $\frac{7}{12}$

Where the marks are

Substitutes the correct values of $sin 6 0^{\circ}$ , $tan 3 0^{\circ}$ and $sec 4 5^{\circ}$ into the expression (1½ marks)
Simplifies to $\frac{7}{12}$ (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 2024-25 (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 sample paper 2024-25: question 23

Hints

Step-by-step solution

Revise the chapter

More questions from Introduction to Trigonometry