Match List I to List II. List I: (A) If x 2 + 4 + 3 sin ( ax + b ) − 2 x = 0 has at least one real root, a , b ∈ [ 0 , 2 π ] , then sin ( a + b ) can equal...; (B) If sin − 1 x ≤ cos − 1 x , then x ca

Question

Match List I to List II. List I: (A) If x 2 + 4 + 3 sin ( ax + b ) − 2 x = 0 has at least one real root, a , b ∈ [ 0 , 2 π ] , then sin ( a + b ) can equal...; (B) If sin − 1 x ≤ cos − 1 x , then 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 and ( sin − 1 y ) 2 − cos − 1 x = π 2 /16 have a common real solution, then n can equal... List II: (P) -1; (Q) 0; (R) 1; (S) 5.

TestHub · Accepted Answer

A: equation is ( x − 1 ) 2 + 3 ( 1 + sin ( a x + b )) = 0 , so x = 1 and sin ( a + b ) = − 1 . B: sin − 1 x ≤ π /4 , so − 1 ≤ x ≤ 1/ 2 ​ ; both -1 and 0 work. C: the two graphs intersect at five points over the stated interval. D: adding gives ( sin − 1 y ) 2 = ( 4 n + 1 ) π 2 /32 and cos − 1 x = ( 4 n − 1 ) π 2 /32 ; imposing 0 ≤ ( sin − 1 y ) 2 ≤ π 2 /4 and 0 ≤ cos − 1 x ≤ π leaves n = 1 .

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

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