This set of Aptitude Questions and Answers (MCQs) focuses on “Height and Distance – Set 3”.
1. What will be the value of (sin 60 + cos 60) – (sin 30 + cos 30)?
a) 1 / 2
b) √3 / 2
c) 0
d) 1
View Answer
Explanation: Given,
(sin 60 + cos 60) – (sin 30 + cos 30)
➩ √3 / 2 + \(\frac {1}{2}-\frac {1}{2}\) – √3 / 2
➩ 0
2. What will be the value of tan 60 / cot 60?
a) 3
b) 1 / 3
c) 1
d) 2√3
View Answer
Explanation: Given,
Tan 60 / cot 60
➩ √3 / (1 / √3)
➩ 3
3. Which of the following is the correct option representing tan2A?
a) Sec2A
b) Sec2A – 1
c) Cosec2A + 1
d) Cot2A
View Answer
Explanation: Given,
Tan2A
According to trigonometric identities,
Tan2A = sec2A – 1
4. If A * cot 45 * cos 60 = sin 60 * tan 30, then what will be the value of A?
a) √3 / 2
b) 0
c) 1
d) 1 / √2
View Answer
Explanation: Given,
A * cot 45 * cos 60 = sin 60 * tan 30
➩ A * 1 * \(\frac {1}{2}\) = √3 / 2 * 1 / √3
➩ A * \(\frac {1}{2} = \frac {1}{2}\)
➩ A = 1
5. What will be the value of sin230 – cos230?
a) -2 / √3
b) -2 / 3
c) -√3 / 2
d) -1 / 2
View Answer
Explanation: Given,
sin230 – cos230
➩ (sin 30 * sin 30) – (cos 30 * cos 30)
➩ (1 / 2 * 1 / 2) – (√3 / 2 * √3 / 2)
➩ \(\frac {1}{4} – \frac {3}{4}\)
➩ -2 / 4 = -1 / 2
6. If X + Y = 90 and cos X = 1 / 2, then what will be the value of sin Y?
a) 1 / 2
b) 1 / √2
c) √3 / 2
d) 0
View Answer
Explanation: Given,
X + Y = 90 and cos X = \(\frac {1}{2}\).
➩ cos 60 = \(\frac {1}{2}\)
➩ X = 60
➩ X + Y = 90
➩ Y = 30
Thus, sin Y = sin 30 = \(\frac {1}{2}\).
7. What will be the value of cos2X + sin2Y?
a) √3 / 2
b) 1 / 2
c) 1
d) √2
View Answer
Explanation: According to trigonometric identity,
cos2X + sin2Y = 1
8. If sec A = 2 / √3, then what will be the value of cos A?
a) 1 / 2
b) √3 / 2
c) 1 / √2
d) 2 / 3
View Answer
Explanation: Given,
sec A = 2 / √3
➩ sec A is complementary of cos A.
Thus, cos A = 1 / sec A
➩ cos A = 1 / (2 / √3)
➩ cos A = √3 / 2
9. Which of the following is a correct trigonometric identity?
a) 1 + tan2 A = sec2 A
b) Tan2 A = sec2 A + 1
c) Cot2 A = cosec2 A – 1
d) Cos2 A + sin2 A = 0
View Answer
Explanation: 1 + tan2 A = sec2 A is the correct option.
The three most common trigonometric identities are:
Cos2 A + sin2 A = 1
1 + tan2 A = sec2 A
Cot2 A + 1 = cosec2 A
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