Match the following. List-I List-II (a) The number of solutions of the equation sin − 1 x + cos − 1 x 2 = 2 π is (p) 1 (b) The number of ordered pairs ( x , y ) satisfying x sin − 1 x = y sin − 1

Question

Match the following. List-I List-II (a) The number of solutions of the equation sin − 1 x + cos − 1 x 2 = 2 π ​ is (p) 1 (b) The number of ordered pairs ( x , y ) satisfying x sin − 1 x ​ = y sin − 1 y ​ = 2 is (q) 2 (c) The number of solutions of the equation cos ( cos x ) = sin ( sin x ) is (r) 0 (d) The number of solutions of the equation tan ( x + 6 π ​ ) = 2 tan x is (s) 3

TestHub · Accepted Answer

(a) cos − 1 x 2 = 2 π ​ − sin − 1 x = cos − 1 x ⇒ x 2 = x ⇒ x = 0 , 1 : 2 solutions (q). (b) x s i n − 1 x ​ ∈ [ 1 , 2 π ​ ] for 0 < ∣ x ∣ ≤ 1 , and 2 π ​ < 2 , so no ordered pair exists (r). (c) cos ( cos x ) = cos ( 2 π ​ − sin x ) ⇒ cos x ± sin x = 2 nπ ± 2 π ​ ; but ∣ cos x ± sin x ∣ ≤ 2 ​ < 2 π ​ , so no solution (r). (d) With y = tan x : 1 − 3 ​ y ​ y + 3 ​ 1 ​ ​ = 2 y ⇒ 2 y 2 − 3 ​ y + 1 = 0 , discriminant 3 − 8 < 0 , no solution (r).

List-I	List-II
(a) The number of solutions of the equation $sin^{- 1} x + cos^{- 1} x^{2} = \frac{π}{2}$ is	(p) 1
(b) The number of ordered pairs $(x, y)$ satisfying $\frac{sin ^{- 1} x}{x} = \frac{sin ^{- 1} y}{y} = 2$ is	(q) 2
(c) The number of solutions of the equation $cos (cos x) = sin (sin x)$ is	(r) 0
(d) The number of solutions of the equation $tan (x + \frac{π}{6}) = 2 tan x$ is	(s) 3

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

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