If A = 5/13, then verify that ( A)/(1 – A) + ( A)/(1 – A) = A + A.

Both sides equal 17/13; verified.

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/3/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2024: question 31(b)

Set in the CBSE Class 10 board exam of 2024, paper 430/3/1, section C, question 31(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31(b) · 3 marks · Short answerIntroduction to Trigonometry

If $cos A = \frac{5}{13}$ , then verify that $\frac{c o s A}{1- t a n A} + \frac{s i n A}{1- c o t A} = cos A + sin A$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/3/1.

Hints

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

Hint 1

Draw a right triangle with adjacent side 5 and hypotenuse 13; find the opposite side.

Hint 2

Compute $1 - tan A$ and $1 - cot A$ carefully before dividing.

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.

$cos A = \frac{5}{13} \Rightarrow sin A = 1 - \frac{25}{169} = \frac{12}{13}$ ; $tan A = \frac{12}{5}$ ; $cot A = \frac{5}{12}$
1½ marks
LHS $= \frac{\frac{5}{13}}{1 - \frac{12}{5}} + \frac{\frac{12}{13}}{1 - \frac{5}{12}} = \frac{\frac{5}{13}}{- \frac{7}{5}} + \frac{\frac{12}{13}}{\frac{7}{12}} = - \frac{25}{91} + \frac{144}{91} = \frac{119}{91} = \frac{17}{13}$
1 mark
RHS $= \frac{5}{13} + \frac{12}{13} = \frac{17}{13}$ . Hence LHS = RHS, verified.
½ mark

Answer: Both sides equal $\frac{17}{13}$ ; verified.

Where the marks are

Finds $sin A = \frac{12}{13}$ , $tan A = \frac{12}{5}$ , $cot A = \frac{5}{12}$ (½ + ½ + ½ marks)
Evaluates LHS $= \frac{17}{13}$ (1 mark)
Evaluates RHS $= \frac{17}{13}$ and concludes (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 paper2024 board paper, set 430/3/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 31(b)

Hints

Step-by-step solution

Revise the chapter

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