If `sec^-1(cos^2x-2cos x +3)+ cosec^-1(5^(cosec^2y)+1)=pi/2.` Then `sin^2x-cos^2y=`

If sec^-1x=cosec^-1y ,then cos^(- 1)(1/x)=cos^(- 1)(1/y)=

If sec^(-1)x=cosec^(-1) y then cos^(-1)(1/x)+cos^(-1)(1/y) =

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

2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)

IF 2 tan ^(-1) (cos x) =tan ^(-1) (2 "cosec"x) then sin x cos x=

If cosec^2x-cot^2y=1 then cos(x-y)=

If sec ^(-1) x=cosec^(-1) y then cos ^(-1) (1)/(x)+cos ^(-1) (1)/(y)=

If y=2 sin^(-1) (cos x)+5"cosec "^(-1) "(sec x). Find"(dy)/(dx) .

If y = sec^(-1) [ "cosec x"] + "cosec"^(-1) [sec x] + sin^(-1) [cos x] + cos^(-1)[sinx ], "then "(dy)/(dx) is equal to