If `sin^2x + sin^2y < 1 ; x, y in R` then prove that `sin^-1(tanx . tany) in (-pi/2, pi/2)`.

If sin^2 x + sin^2 y = 1 , then what is the value of cot (x + y) ?

If sin^(2)x+sin^(2)y=1 , then what is the value of cot(x+y) ?

Show that sin(x+y)sin(x-y)= sin^2 x -sin^2 y .Hence prove that sin(x+y)sin(x-y)+sin(y+z)sin(y-z) +sin(z+x)sin(z-x)=0

If sin ^ (2) x + sin ^ (2) y <1; x, y in R then prove that sin ^ (- 1) (tan x.tan y) in (- (pi) / (2), ( pi) / (2))

If sin2x=n sin 2y , then the value of (tan(x+y))/(tan(x-y)) is :

If sin 2 x=n sin 2 y then the value of (tan (x+y))/(tan (x-y))=

Differentiate sin2x = sin2y with respect to x

If x+y+z= (pi)/(2) show that sin 2x + sin 2y + sin 2z =4 cos x cosy cos z