Match List I to List II. List I: (A) Number of solutions of y = ∣ sin x ∣ and y = cos − 1 ( cos x ) , − 4 π ≤ x ≤ 4 π ; (B) If sin − 1 x ≤ cos − 1 x , x can equal...; (C) Number of ordered pairs ( x ,

Question

Match List I to List II. List I: (A) Number of solutions of y = ∣ sin x ∣ and y = cos − 1 ( cos x ) , − 4 π ≤ x ≤ 4 π ; (B) If sin − 1 x ≤ cos − 1 x , x can equal...; (C) Number of ordered pairs ( x , y ) satisfying ∣ y ∣ = cos x and y = sin − 1 ( sin x ) , − 2 π ≤ x ≤ 3 π ; (D) If n ∈ N and cos − 1 x + ( sin − 1 y ) 2 = n π 2 /4 , ( sin − 1 y ) 2 − cos − 1 x = π 2 /16 are consistent, n can equal... List II: (P) 1; (Q) 0; (R) 4; (S) 5.

TestHub · Accepted Answer

A: On each interval [ 2 k π , ( 2 k + 1 ) π ] , cos − 1 ( cos x ) rises from 0 to π , while ∣ sin x ∣ ≤ 1 , so only the zeros at x = 2 k π coincide. There are five such x in [ − 4 π , 4 π ] . B: sin − 1 x ≤ cos − 1 x is satisfied at x = 0 . C: plot the graphs on [ − 2 π , 3 π ] and count five intersections. D: the two equations give ( sin − 1 y ) 2 = ( 4 n + 1 ) π 2 /32 and cos − 1 x = ( 4 n − 1 ) π 2 /32 ; the principal ranges leave n = 1 .

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

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