" Prore that: "sin^(-1)(2sqrt(2))/(3)+sin^(-1)1/3=pi/2

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

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

Prove that sin^-1 (-(sqrt3)/(2)) = - (pi/3)

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)))

Consider the following statements : 1. There exists theta in(-(pi)/(2),(pi)/(2)) for which tan^(-1)(tan theta) ne theta . 2. sin^(-1)((1)/(3))-sin^(-1)((1)/(5))=sin^(-1)((2 sqrt(2)(sqrt(3)-1))/(15)) Which of the above statements is/are correct?

If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)/2)+cos^(-1)(1/3) then

If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)/2)+cos^(-1)(1/3) then

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)))