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What is (sin x cos y + cos x sin y)(sin x cos y - cos x sin y) equal to?

A) \( cos^{2}x - cos^{2}y\)
B) \( cos^{2}x - sin^{2}y\)
C) \( sin^{2}x - cos^{2}y\)
D) \( sin^{2}x - sin^{2}y\)

Correct Answer:




D) \( sin^{2}x - sin^{2}y\)

Description for Correct answer:
(sinx cosy + cosx siny)(sinx cosy - cosx siny)

= sin(x + y).sin(x - y)

\( \Large = sin^{2}x - sin^{2}y \)

option d is correct

Part of solved CDS Maths(1) questions and answers : Exams >> CDSE >> CDS Maths(1)

Comments

Similar Questions

1). what is (1 + cot x - cosec x)(1 + tan x + cot x) equal to?

A). Sin x + cos x

B). Sin x - cos x

C). 2

D). 1

2). What is (cosec x - sin x)(sec x - cos x)(tan x + cot x)equal to?

A). Sin x + cos x

B). Sin x - cos x

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D). 1

3). Consider the following statements:
1. \(Sin 1^{\circ} > Sin 1\)
2. \(Cos 1^{\circ} < Cos 1\)
Which of the above statements is/are correct?

A). 1 only

B). 2 only

C). Both 1 and 2

D). Neither 1 nor 2

4). If sin x + cosec x = 2, then what is \(sin^{9}x + cosec^{9}x\) equal to ?

A). 2

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C). 512

D). 1024

5). If sin x + cos x = p and \( sin^{3}x + cos^{3}x = q\), then what is p^{3} - 3p equal to ?

A). 0

B). -2q

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D). 4q

6). What is the number of pairs of perpendicular planes in cuboid?

A). 4

B). 8

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7). How many equilateral triangles can be formed by joining any three vertices of a cube?

A). 0

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8). For the next two (2) items that follow :
ABCD is a trapezium in which AB is parallel to CD. Let M be the midpoint of BC.
68. Consider the following statements :
1. 'Area of triangle ADM + Area of triangle DCM' is equal to three-fourth of the area of trapezium ABCD, if AB = CD.
2. 'Area of triangle DCM + Area of triangle ABM' is always greater than half of the area of trapezium ABCD.
Which of the above statements is/are correct?

A). 1 only

B). 2 only

C). Both 1 and 2

D). Neither 1 nor 2

9). Consider the following statements :
1. 'Area of triangle ADM Area of triangle ABM' is always equal to area of triangle DCM, if AB = CD.
2. Half of area of triangle ABM is equal to one-eighth of area of trapezium ABCD. if AB = CD
Which of the above statements is/are correct?

A). 1 only

B). 2 only

C). Both 1 and 2

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10). ABCD is a parallelogram. P and R are the midpoints of DC and BC respectively. The line PR intersects the diagonal AC at Q. The distance CQ will be equal to

A). \( \Large \frac{AC}{4} \)

B). \( \Large \frac{BD}{3} \)

C). \( \Large \frac{BD}{4} \)

D). \( \Large \frac{AC}{3} \)