Match the following :
Column I | Column II |
(i) Let ABCDEFGHIJKL is a regular dodecagon then value of + is | [A] 3 |
(ii) equals | [B] 10 |
(iii) No. of solutions of tan 3x – tan 2x – tanx = 0 in [0, π) is | [C] 4 |
(iv) sides of a ΔABC are 5, 12, 13 cm. The radius of escribed circle touching side of length 12 cm is | [D] 5 |
Text Solution
Verified by Experts(i) [C]; (ii) [C]; (iii) [A]; (iv) [B]
Ans.
(i) [C]
(ii) [C]
(iii) [A]
(iv) [B]
Sol. (i) AM = R sin 15°
AB = 2 R sin 15°
Similarly AN = R sin 75°
∴ AF = 2R sin 75°
∴ 
+ 
= 
+ 
= tan 15° + cot 75° = 4
(ii) 
= 
= 
= 4
(iii) tan 3x – tan 2x – tan x = 0
⇒ tan 3x. tan 2x. tan x = 0
∴ x = 
, x = 
, x = n π
But x ≠ (2n + 1) 
as tan x is not defined
∴ combining all x = n π /3 , n ∈ Z
∴ solution in [0, π ) is 0, π /3, 2 π /3
(iv) user = 
where Δ = 30, s = 15, a = 12
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