Match the column :
Column-I | Column-II |
(i) No. of solutions of equation | cot x | = cot x + (0 < x < π) is/are | [A] No solution |
(ii) If sinθ + sinφ = & cosθ + cosφ = 2 then cot is | [B] 1 |
(iii) sin2 α + sin . Sin equals | [C] |
(iv) If tanθ = 3 tan φ then max. value of tan2 (θ – φ) is | [D] |
Text Solution
Verified by Experts(i) [B]; (ii) [A]; (iii) [D]; (iv) [C]
Ans.
(i) [B]
(ii) [A]
(iii) [D]
(iv) [C]
Sol. (i) |cot x| = cot x + 
if 0 < x < 
then 
= 0 is not possible
If 
< x < π 2 cot x + 
= 0 cos x = 
⇒ x = 
⇒ only one solution
(ii) If cos θ + cos φ = 2
then θ = φ = 2n π
But sin θ + sin φ = 
(not possible)
(iii) Do yourself
(iv) tan ( θ – φ ) = 
= 
= 
(for max. tan φ > 0)
∴ using A. M. ≥ G.M.
cot φ + 3 tan φ ≥ 
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