((5)/(²θ) - (5)/(²θ) ) is equal to : (A) 1 (B) 5 (C) -5 (D) 0

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2024: question 10

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, section A, question 10, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q10 · 1 mark · MCQIntroduction to Trigonometry

$(\frac{5}{c o t ^{2} θ} - \frac{5}{c o s ^{2} θ})$ is equal to :

(A)1
(B)5
(C) $- 5$
(D)0

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/5/1.

Hints

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

Hint 1

Write $1/ cot^{2} θ$ and $1/ cos^{2} θ$ as other ratios.

Hint 2

Use $1 + tan^{2} θ = sec^{2} θ$ .

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.

$\frac{5}{c o t ^{2} θ} - \frac{5}{c o s ^{2} θ} = 5 tan^{2} θ - 5 sec^{2} θ = 5 (tan^{2} θ - sec^{2} θ)$ .
Since $sec^{2} θ - tan^{2} θ = 1$ , value $= 5 (- 1) = - 5$ .
1 mark

Answer: $- 5$ , option (C)

Where the marks are

Converts to $5 (tan^{2} θ - sec^{2} θ)$ and uses identity to get $- 5$ (1 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 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 10

Hints

Step-by-step solution

Revise the chapter

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