sin^(−1)⁡x=cos^(−1)⁡√(1−x^2 )

The number of integer x satisfying sin^(-1)|x-2|+cos^(-1)(1-|3-x|)=pi/2 is 1 (b) 2 (c) 3 (d) 4

The number of roots of the equation sin^(-1)x-(1)/(sin^(-1)x)=cos^(-1)x-(1)/(cos^(-1)x) is (a) 0 (b) 1 (c) 2 (d) 3

Solve sin^(-1)x-cos^(-1)x=sin^(-1)(3x-2)

Solve sin^(-1)x-cos^(-1)x=sin^(-1)(3x-2)

(d(sin^(-1)x))/(d(cos^(-1)sqrt(1-x^(2))))=?

Range of f(x)=sin^(-1)[x-1]+2cos^(-1)[x-2] ([.] denotes greatest integer function)

Statement -1: If a is twice the tangent of the arithmetic mean of sin^(-1)x and cos^(-1) x , b the geometric mean of tanx and cot x then x^(2)-ax+b=0rarr x=1 statement-2: tan((sin^(-1)x+cos^(-1)x)/(2))=1

Let t_(1)= (sin^(-1)x)^(sin^(-1)x),t_(2)= (sin^(-1) x)^(cos^(-1)x),t_(3) = (cos^(-1)x)^(sin^(-1)x),t_(4) = (cos^(-1)x)^(cos^(-1)x) , Match the follwing items of Column I with Column II

The range of the function f(x) = sin^(-1)[x^2+1/2]+cos^(-1)[x^2-1/2] , where [ . ] denotes the greatest integer function.

STATEMENT-1 : If tan^2 (sin^-1x) > 1 then x in(-1-1/sqrt2)uu(1/sqrt(2).1). STATEMENT-2 : The number of positive integral solution of tan^-1 1/y+cot^-1(1/x)=cot^-1(1/3), where x/y < 1, is 2. STATEMENT -3 : If sin^-1 x=-cos^-1 sqrt(1-x^2) and sin^-1 y=cos^-1 sqrt(1-y^2), then the exact range of (tan^-1 x+ tan6-1 y) is [-pi/4,pi/4].