" सिद "vec oodot x*vec sin^(-1)((2sqrt(2))/(3))+sin^(-1)((1)/(3))=(pi)/(2)

sin ^(-1) (sqrt(3))/(2) + sin ^(-1) sqrt(2/3)=

sin ^(-1)sqrt(3)x+sin ^(-1)x=(pi)/(2)

Show that "sin"^(-1)(sqrt(3))/2+"tan"^(-1)1/(sqrt(3))=(2pi)/3

Find the principal value of each of the following: sin^(-1)(-(sqrt(3))/(2))( (ii) sin^(-1)((cos(2 pi))/(3))( iii) sin^(-1)((sqrt(3)-1)/(2sqrt(2)))

Find the principal value of each of the following: (i) sin^(-1)(-(sqrt(3))/2) (ii) sin^(-1)(cos (pi/3)) (iii) sin^(-1)((sqrt(3)-1)/(2sqrt(2)))

Find the principal value of each of the following: sin^(-1)((sqrt(3)+1)/(2sqrt(2)))( (ii) sin^(-1)((cos(3 pi))/(4))( iii) sin^(-1)((tan(5 pi))/(4))

A value of for which (2+3isintheta)/(1-2isintheta) purely imaginary, is : (1) pi/3 (2) pi/6 (3) sin^(-1)((sqrt(3))/4) (4) sin^(-1)(1/(sqrt(3)))

Let f:[-pi/3,(2pi)/3]vec[0,4] be a function defined as f(x)=sqrt(3)sinx-cosx+2. Then f^(-1)(x) is given by (a) sin^(-1)((x-2)/2)-pi/6 (b) sin^(-1)((x-2)/2)+pi/6 (c) (2pi)/3+cos^(-1)((x-2)/2) (d) none of these

If sin^(-1)((sqrt(x))/2)+sin^(-1)(sqrt(1-x/4))+tan^(-1)y=(2pi)/3 , then