Match the following. List I List II (A) sin ( π x / ( 2 3 )) = x 2 − 2 3 x + 4 (P) 4 (B) sin 4 x = 1 + tan 8 x (Q) 1 (C) cos 2 x = ∣ sin x ∣ , x ∈ ( − π /2 , π ) (R) 3 (D) n ∣ sin x ∣ = m ∣ cos x

Question

Match the following. List I List II (A) sin ( π x / ( 2 3 ​ )) = x 2 − 2 3 ​ x + 4 (P) 4 (B) sin 4 x = 1 + tan 8 x (Q) 1 (C) cos 2 x = ∣ sin x ∣ , x ∈ ( − π /2 , π ) (R) 3 (D) n ∣ sin x ∣ = m ∣ cos x ∣ on [ 0 , 2 π ] , with integers n > m > 0 (S) 0

TestHub · Accepted Answer

A: RHS is (x - √3)² + 1, so equality requires x = √3 and LHS = 1. B: equality would require sin⁴x = 1 and tan x = 0 simultaneously, impossible. C: sin x = 1/2 at π/6 and 5π/6, or sin x = -1/2 at -π/6: three. D: the absolute-value curves intersect four times on [0, 2π].

Mathematics - Trigonometric Equation Question with Solution | TestHub

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Doubts & Discussion

List I	List II
(A) $sin (π x / (23)) = x^{2} - 23 x + 4$	(P) 4
(B) $sin^{4} x = 1 + tan^{8} x$	(Q) 1
(C) $cos 2 x = ∣ sin x ∣$ , $x \in (- π /2, π)$	(R) 3
(D) $n ∣ sin x ∣ = m ∣ cos x ∣$ on $[0, 2 π]$ , with integers $n > m > 0$	(S) 0