Prove that : √((1 + A)/(1 - A)) = A + A

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 23(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section B, question 23(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(a) · 2 marks · Very short answerIntroduction to Trigonometry

Prove that : $\frac{1 + s i n A}{1 - s i n A} = sec A + tan A$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

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

Hint 1

Make the expression under the root a perfect square by multiplying top and bottom by the same factor.

Hint 2

Multiply by $\frac{1 + s i n A}{1 + s i n A}$ and use $1 - sin^{2} A = cos^{2} A$ .

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.

LHS $= \frac{1 + sin A}{1 - sin A} \times \frac{1 + sin A}{1 + sin A}$ (rationalising).
½ mark
$= \frac{( 1 + sin A ) ^{2}}{1 - sin ^{2} A} = \frac{1 + sin A}{1 - sin ^{2} A}$
½ mark
$= \frac{1 + sin A}{cos A}$ [since $1 - sin^{2} A = cos^{2} A$ ]
½ mark
$= \frac{1}{cos A} + \frac{sin A}{cos A} = sec A + tan A =$ RHS. Hence proved.
½ mark

Answer: LHS $= \frac{1 + sin A}{cos A} = sec A + tan A =$ RHS

Where the marks are

Multiplies numerator and denominator by $1 + sin A$ (½ mark)
Gets $\frac{1 + s i n A}{1 - s i n ^{2} A}$ (½ mark)
Uses $1 - sin^{2} A = cos^{2} A$ (½ mark)
Splits into $sec A + tan A$ (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 paper2026 board paper, set 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 23(a)

Hints

Step-by-step solution

Revise the chapter

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