Column I, Column II ( sin − 1 x ) 2 + ( y ) 2 = π 2 2 x 3 + y 3 = , p. 1 ( cos − 1 x ) 2 + ( cos − 1 y ) 2 = 2 π 2 x 5 + y 5 = , q. − 2 ( sin − 1 x ) 2 ( cos − 1 y ) 2 = pi 4 4 | x − y | , r. 0 ∣ ∣ sin − 1 x − sin − 1 y = π x y = , s. 2

If sin x + sin y = 1/2 and cos x + cos y = 1 then tan (x + y)

If sin −1 x+sin −1 y+sin −1 z=π, prove that x 1−x 2 ​ +y 1−y 2 ​ +z 1−z 2 ​ =2xyz.

If (dy)/(dx)-y log_(e) 2 = 2^(sin x)(cos x -1) log_(e) 2 , then y =

If tan ^(-1) x + tan ^(-1) .sqrt( 1 - y^(2))/y = pi/3 " and " sin^(-1) y - cos^(-1) ( x/(sqrt( 1 + x^(2)))) = pi/6 " , then " ( 5 sin^(-1) x)/( sin^(-1) y) is

If sin^-1 x + sin^-1 y = (2pi)/3, then cos^-1 x + cos^-1 y =

If y= y(x) ( 2 _ cos x ) /( y+1) (( dy )/(dx)) =- sin x, y (0) =1 then y((pi)/(2)) equal ____.

Let (x , y) be such that sin^(-1)(a x)+cos^(-1)(y)+cos^(-1)(b x y)=pi/2dot Match the statements in column I with statements in column II Ifa=1a n db=0,t h e n(x , y) , (p) lies on the circle x^2+y^2=1 Ifa=1a n db=1,t h e n(x , y) , (q) l i e son(x^2-1)(y^2-1)=0 Ifa=1a n db=2,t h e n(x , y) , (r) lies on y=x Ifa=2a n db=2,t h e n(x , y) , (s) lies on (4x^2-1)(y^2-1)=0

Solve the equation : sin (x-y) = sqrt(3)/2 and cos (x+y) = 1/2

Suppose 3 sin^(-1) ( log _(2) x) + cos^(-1) ( log _(2) y) =pi //2 and sin^(-1) ( log _(2) x ) + 2 cos^(-1) ( log_(2) y) = 11 pi //6 . then the value of 1/x^(-2) + 1/y^(-2) equals .

If y=(sin^(-1)x)^2 , prove that (1-x^2)y_2-x y_1-2=0 .