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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

Correct Answer:


B) Sin x - cos x

Description for Correct answer:
(1 + cotx - cosecx)( 1 + tanx + secx)

Let x = 30 deg then

\( \Large =(1 + \sqrt{3} - 2) \left(1 + \frac{1}{3} + \frac{2}{\sqrt{3}}\right) \)

\( \Large = (\sqrt{3} - 1) \left( \frac{3 + \sqrt{3}}{\sqrt{3}} \right) \)

\( \Large (\sqrt{3} - 1)(\sqrt{3} + 1) \)

= 2

Option (B) is correct.

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

Comments

Similar Questions

1). 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

C). 2

D). 1

2). 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

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

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4). 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

C). 2q

D). 4q

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

A). 4

B). 8

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D). None of these

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

A). 0

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7). 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 :
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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

8). 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

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

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1. The altitudes are congruent.
2. The three medians are congruent.
3. The centroid bisects the altitude.
Which of the above statements are correct?

A). 1 and 2 only

B). 2 and 3 only

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