Use the identity: ² A + ² A = 1 to prove that ² A + 1 = ² A. Hence, find the value of A, when A = 5/3, where A is an acute angle.

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 22(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, section B, question 22(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

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

Use the identity: $sin^{2} A + cos^{2} A = 1$ to prove that $tan^{2} A + 1 = sec^{2} A$ . Hence, find the value of $tan A$ , when $sec A = \frac{5}{3}$ , where A is an acute angle.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

Which trigonometric ratio squared would turn $sin^{2} A$ into $tan^{2} A$ ?

Hint 2

Divide every term by $cos^{2} A$ , then put $sec A = 5/3$ in the result.

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.

Dividing $sin^{2} A + cos^{2} A = 1$ by $cos^{2} A$ ( $cos A \neq = 0$ ): $\frac{sin ^{2} A}{cos ^{2} A} + \frac{cos ^{2} A}{cos ^{2} A} = \frac{1}{cos ^{2} A}$
½ mark
$\Rightarrow tan^{2} A + 1 = sec^{2} A$ . Hence proved.
½ mark
Given $sec A = \frac{5}{3}$ : $tan^{2} A = (\frac{5}{3})^{2} - 1 = \frac{25}{9} - 1 = \frac{16}{9}$
½ mark
Since A is acute, $tan A > 0$ , so $tan A = \frac{4}{3}$ .
½ mark

Answer: $tan A = \frac{4}{3}$

Where the marks are

Divides the identity by $cos^{2} A$ (½ mark)
Obtains $tan^{2} A + 1 = sec^{2} A$ (½ mark)
Substitutes $sec A = 5/3$ (½ mark)
Gets $tan A = 4/3$ (½ mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Proving Simple Trigonometric Identities

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 30/6/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 22(b)

Hints

Step-by-step solution

Revise the chapter

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