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 tan^{2}A?

a) Sec^{2}A

b) Sec^{2}A – 1

c) Cosec^{2}A + 1

d) Cot^{2}A

View Answer

Explanation: Given,

Tan

^{2}A

According to trigonometric identities,

Tan

^{2}A = sec

^{2}A – 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 sin^{2}30 – cos^{2}30?

a) -2 / √3

b) -2 / 3

c) -√3 / 2

d) -1 / 2

View Answer

Explanation: Given,

sin

^{2}30 – cos

^{2}30

➩ (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 cos^{2}X + sin^{2}Y?

a) √3 / 2

b) 1 / 2

c) 1

d) √2

View Answer

Explanation: According to trigonometric identity,

cos

^{2}X + sin

^{2}Y = 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 + tan^{2} A = sec^{2} A

b) Tan^{2} A = sec^{2} A + 1

c) Cot^{2} A = cosec^{2} A – 1

d) Cos^{2} A + sin^{2} A = 0

View Answer

Explanation: 1 + tan

^{2}A = sec

^{2}A is the correct option.

The three most common trigonometric identities are:

Cos

^{2}A + sin

^{2}A = 1

1 + tan

^{2}A = sec

^{2}A

Cot

^{2}A + 1 = cosec

^{2}A

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