Match the following. List I List II (A) Number of roots of ∣ cot x ∣ = cot x + 1/ sin x , 0

Question

Match the following. List I List II (A) Number of roots of ∣ cot x ∣ = cot x + 1/ sin x , 0 < x < π (P) No solution (B) If sin θ + sin ϕ = 1/2 and cos θ + cos ϕ = 2 , value of cot (( θ + ϕ ) /2 ) (Q) 1/3 (C) sin 2 α + sin ( π /3 − α ) sin ( π /3 + α ) (R) 1 (D) Maximum of tan 2 ( θ − ϕ ) when tan θ = 3 tan ϕ (S) 3/4 (T) 4

TestHub · Accepted Answer

A: x = 2π/3 only. B: the cosine sum can be 2 only if both cosines are 1; then their sine sum is 0, not 1/2, so no solution. C: sin(u-v)sin(u+v) = sin²u - sin²v gives sin²(π/3) = 3/4. D: putting t = tan φ gives tan(θ-φ) = 2t/(1+3t²); its squared maximum is 1/3.

List I	List II
(A) Number of roots of $∣ cot x ∣ = cot x + 1/ sin x$ , $0 < x < π$	(P) No solution
(B) If $sin θ + sin ϕ = 1/2$ and $cos θ + cos ϕ = 2$ , value of $cot ((θ + ϕ) /2)$	(Q) $1/3$
(C) $sin^{2} α + sin (π /3 - α) sin (π /3 + α)$	(R) 1
(D) Maximum of $tan^{2} (θ - ϕ)$ when $tan θ = 3 tan ϕ$	(S) $3/4$
	(T) 4

Mathematics - Trigonometric Equation Question with Solution | TestHub

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