Match the following :
Column-I | Column-II |
(i) Period of cos 2πx + [2x] + [–2x] is | [A] 4 |
(ii) tan is equal to | [B] 3 |
(iii) 4 + [sin–1sinr] is equal to | [C] 2 |
(iv) If tan–1 = 2 sin–1then x is (where [⋅⋅] denotes greatest integer function) | [D] 1 |
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) - [D]
(ii) - [B]
(iii) - [C]
(iv) - [C]
Sol. (i) f(x) = cos2 π x + 2x – {2x} + (–2x – {–2x})
= cos2 π x – {2x} – {–2x}
↓ ↓ ↓
Period 1 1/2 1/2
LCM of 
= 1
∴ f(x) is periodic with period 1
(ii) 
tan 
=3
(iii) 4 + 
[sin –1 sinr] = 4 + [sin –1 (sin1)] + [sin –1 (sin2)] + ……...+……... [sin –1 (sin10)]
= 4 + {1 + 1 + 0 + (–1) + (–2) + (–1) + 0 + 1 + 0 + (–1)}
= 2
(iv) tan –1 
= 2 sin –1 
Let sin –1 
= θ ⇒ sin θ = 
or tan θ = 
∴ tan –1 
= 2 θ ⇒ 
= tan2 θ
⇒ 
= 
⇒ x = 2
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