Match the following. List I List II (A) Number of solutions of tan x + sec x = 2 cos x on [ 0 , 2 π ] (P) 4 (B) Number of real solutions of x 2 l o g x ( x + 3 ) = 16 (real logarithms) (Q) π /2 (C)

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Match the following. List I List II (A) Number of solutions of tan x + sec x = 2 cos x on [ 0 , 2 π ] (P) 4 (B) Number of real solutions of x 2 l o g x ​ ( x + 3 ) = 16 (real logarithms) (Q) π /2 (C) Best λ such that the area of every triangle satisfies Δ ≤ ( b 2 + c 2 ) / λ (R) 2 (D) Common difference if the four solutions of ∣ sin θ ∣ = k in [ 0 , 2 π ] are in A.P (S) 0 (T) π /3

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A: 1 + sin x = 2 cos²x gives sin x = 1/2 (sin x = -1 has cos x = 0 and is invalid), thus two. B: x > 0, x ≠ 1; (x+3)² = 16 gives x = 1 or -7, neither valid, thus zero. C: Δ = bc sin A/2 ≤ (b²+c²)/4, equality when b = c and A = π/2, hence 4. D: four equally spaced roots occur when k = √2/2, at π/4, 3π/4, 5π/4, 7π/4, gap π/2.

List I	List II
(A) Number of solutions of $tan x + sec x = 2 cos x$ on $[0, 2 π]$	(P) 4
(B) Number of real solutions of $x^{2 l o g_{x} (x + 3)} = 16$ (real logarithms)	(Q) $π /2$
(C) Best $λ$ such that the area of every triangle satisfies $Δ \leq (b^{2} + c^{2}) / λ$	(R) 2
(D) Common difference if the four solutions of $∣ sin θ ∣ = k$ in $[0, 2 π]$ are in A.P	(S) 0
	(T) $π /3$

Mathematics - Trigonometric Equation Question with Solution | TestHub

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