Equations `2 sin^-1 x + 3 sin^-1y = (5pi)/2 and y = kx-5` hold simultaneously when k equals (A) 2 (B) 4 (C) 6 (D) no such k exists

Suppose that for some angles x and y the equations sin^(2)x+cos^(2)y=(3a)/(2) , cos^(2)x+sin^(2)y=(a^(2))/(2) hold simultaneously then the value of cos2x-cos2y equals (A) a (B) 2-a (C) 3a-2 (D) 2a-3

If sin^(-1)x+sin^(-1)y=pi and x=ky then find the value of (39)^(2k)+5^(k)

If sin^(-1)x+sin^(-1)y=(2 pi)/(3) ,then the value of cos^(-1)x+cos^(-1)y is (A) (2 pi)/(3) (B) (pi)/(3) (C) (pi)/(2) (D) pi

If sin^(-1)(tan(pi)/4)-sin^(-1)(sqrt(3/y))-(pi)/6=0 and x^(2)=y then x is equal to

If sin^(-1)(tan(pi/4))-sin^(-1)(sqrt(3/y))-(pi)/6=0 and x^(2)=y then x is equal to

Given sin B =1/5*sin (2A +B) then tan (A +B)= k tan A, where k has the value equal to ............... A) 5/3 B) 2/3 C) 3/2 D) 3/5

If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi/2 then the value of x^2+y^2+z^2+2xyz is equal to a)0 b)1 c)2 d)3

If a=sin pi/18 sin 5pi/18 sin(7pi)/18 and x is the solution of the equation y=2[x]+2 and y=3[x-2], where [x] denotes the interal part of x then a= (A) [x] (B) 1/ [x] (C) 2[x] (D) [x]^2

If cos3x+sin(2x-(7pi)/6)=-2 , then x is equal to (k in Z) pi/3(6k+1) (b) pi/3(6k-1) pi/3(2k+1) (d) none of these

If a=sin\ pi/18 sin\ (5pi)/18 sin\ (7pi)/18, and x is the solution of the equation y=2[x]+2 and y=3[x-2], where [x] denotes the integral part of x then a= (A) [x] (B) 1/[x] (C) 2[x] (D) [x]^2