TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES (CDS)

Total Questions: 108

1. If cos² x + cos x = 1 then what is the value of sin¹² x + 3sin¹⁰ x + 3sin⁸ x + sin⁶ x ? [2019 (II) Evening Shift]

Correct Answer: (a) 1
Solution:Given, cos² x + cos x = 1

2. Solve the following equation [2019 (II) Evening Shift]

Correct Answer: (d) 1365
Solution:Given, sinθ = 3/5


3. Solve the following equation [2019 (II) Evening Shift]

Correct Answer: (c) 2
Solution:

4. If tan x = 1 0 < x < 90° , then what is the value of 2sin cos x [2019 (I) Morning Shift]

Correct Answer: (b) 1
Solution:Given, tan x = 1 0 < x < 90°

5. What is the value of sin 46° cos 44° + cos 46° sin 44° ? [2019 (I) Morning Shift]

Correct Answer: (c) 1
Solution:Given, sin 46° cos 44° + cos 46° sin 44°

6. Suppose 0 < θ < 90°, then for every θ, 4sin² θ + 1 is greater than or equal to [2019 (I) Morning Shift]

Correct Answer: (a) 2
Solution:

7. What is the value of tan 1° tan 2° tan 3° ... tan 89° ? [2019 (I) Morning Shift]

Correct Answer: (b) 1
Solution:Given, tan 1° tan 2° tan 3° ... tan 89°

8. There are two parallel streets each directed North to South. A person in the first street travelling from South to North wishes to take the second street which is on his right side. At some place, he makes a 150° turn to the right and he travels for 15 min at the speed of 20 km/h. After that he takes a left turn of 60° and travels for 20 min at the speed of 30 km/h in order to meet the second street. What is the distance between the two streets? [2019 (I) Morning Shift]

Correct Answer: (c) 12.5 km
Solution:There are two parallel streets.


9. If 3tan θ = cot θ where 0 ≤ θ < π/2, then what is the value of θ? [2019 (I) Morning Shift]

Correct Answer: (a) π/6
Solution:Given, 3tan θ = cot θ 0 ≤ θ < π/2

10. What is the value of sin² 25° + sin² 65° ? [2019 (I) Morning Shift]

Correct Answer: (b) 1
Solution: