Evaluate: 2² 45°+ ² 30°- ² 90°.

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 22(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/5/1, section B, question 22(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(a) · 2 marks · Very short answerIntroduction to Trigonometry

Evaluate: $2 tan^{2} 4 5^{\circ} + cos^{2} 3 0^{\circ} - sin^{2} 9 0^{\circ}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/5/1.

Hints

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

Hint 1

Recall the values of $tan 4 5^{\circ}$ , $cos 3 0^{\circ}$ and $sin 9 0^{\circ}$ from the trigonometric table.

Hint 2

Square each value first, then add and subtract.

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 the standard values $tan 4 5^{\circ} = 1$ , $cos 3 0^{\circ} = \frac{3}{2}$ , $sin 9 0^{\circ} = 1$ :
$2 (1)^{2} + (\frac{3}{2})^{2} - (1)^{2}$
1½ marks
$= 2 + \frac{3}{4} - 1 = \frac{7}{4}$
½ mark

Answer: $\frac{7}{4}$

Where the marks are

Substitutes correct values of $tan 4 5^{\circ}$ , $cos 3 0^{\circ}$ , $sin 9 0^{\circ}$ (1½ marks)
Simplifies to $\frac{7}{4}$ (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 paper2025 board paper, set 430/5/1 (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 2025: question 22(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Introduction to Trigonometry