Prove that ( A – A)/( A + A) = ( A – A)/( A + A)

LHS = (1- A)/(1+ A) = RHS; identity proved.

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2026: question 28(a)

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section C, question 28(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28(a) · 3 marks · Short answerIntroduction to Trigonometry

Prove that $\frac{c o t A - c o s A}{c o t A + c o s A} = \frac{s e c A - t a n A}{s e c A + t a n A}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

Express everything in terms of sin A and cos A.

Hint 2

Take $cos A$ common in numerator and denominator of the LHS.

Hint 3

To bring in sec A and tan A, divide numerator and denominator by $cos A$ .

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 $= \frac{\frac{c o s A}{s i n A} - c o s A}{\frac{c o s A}{s i n A} + c o s A} = \frac{c o s A - s i n A c o s A}{c o s A + s i n A c o s A}$ (multiplying numerator and denominator by $sin A$ )
1 mark
$= \frac{c o s A ( 1 - s i n A )}{c o s A ( 1 + s i n A )} = \frac{1 - s i n A}{1 + s i n A}$
½ mark
Dividing numerator and denominator by $cos A$ : $= \frac{\frac{1}{c o s A} - \frac{s i n A}{c o s A}}{\frac{1}{c o s A} + \frac{s i n A}{c o s A}}$
1 mark
$= \frac{s e c A - t a n A}{s e c A + t a n A} =$ RHS. Hence proved.
½ mark

Answer: LHS = $\frac{1 - s i n A}{1 + s i n A}$ = RHS; identity proved.

Where the marks are

Writes cot A as $\frac{c o s A}{s i n A}$ and simplifies (1 mark)
Reduces to $\frac{1 - s i n A}{1 + s i n A}$ (½ mark)
Divides by $cos A$ (1 mark)
Obtains $\frac{s e c A - t a n A}{s e c A + t a n A}$ (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 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 28(a)

Hints

Step-by-step solution

Revise the chapter

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