If `alpha=3sin^-1(6/11) `and `beta=3cos^-1(4/9)`, where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)

If alpha=3sin^(-1)(6/11) and beta=3 cos^(-1)(4/9) where the inverse trigoometric functions take only the principal values, then the correct options (s) is (are)

If alpha = 3 sin^(-1) ((6)/(11) and beta = 3 cos^(-1) ((4)/(9)) , where the inverse trigonometric functions take only the principal values, then the correct options (s) is (are)

If alpha = 3 sin ^(-1) ""((6)/(11) )and beta =3 cos ^(-1)""((4)/(9)) , where the inverse trigonometric function take only the priencipal values , then the correct option (s) is are -

cos^(-1) (cos (-5)) + sin^(-1) (sin(6)) - tan^(-1)(tan (12)) is equal to : (The inverse trigonometric functions take the principal values)

cos^(-1) (cos (-5)) + sin^(-1) (sin(6)) - tan^(-1)(tan (12)) is equal to : (The inverse trigonometric functions take the principal values)

Transform sin^(-1)x in other inverse trigonometric function,where x in(-1,1)-(0)

If alpha=3sin^(-1)(2/3) and beta=2cos^(-1)(1/3) then which of the following is/are CORRECT?

Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy sin^(-1)((3x)/(5))+sin^(-1)((4x)/(5))=sin^(-1)x is equal to :

If we consider only the principal values then the value inverse trigonometric functions then the value of tan(cos^(-1)(1/(5sqrt2)) -sin^(-1)(4/sqrt17)) is

If we consider only the principal values then the value inverse trigonometric functions then the value of (cos^-1(1/(5sqrt2) (-sin^-1)4/sqrt(17)) is (a) sqrt(29)/3 (b) 29/3 (c) sqrt3/29 (d) 3/29