Is my answer for 3 and 4 correct please if not solve plz Is

Is my answer for 3 and 4 correct please if not solve plz tan (cos^-1(1/3))= sin (tan^-1(-3))

Solution

3) . tan(cos^-1 (1/3))

let cos^-1(1/3) = x

then cosx = 1/3

sin^2 x = 1 -cos^2x = 1 - 1/9

sinx = 2sqrt(2)/3

tanx = sinx/cosx

= 2sqrt(2)/3 /1/3

= 2sqrt(2) ( your ans is correct but it should be in numerator)

4).

sin(tan^-(-3))

let tan^-1 (3)=x

then tanx = 3

sec^2 x = 1+tan^2x = 1+3^2 =10

secx = sqrt(10)

cosx = 1/sqrt(10)

sin^2 x = 1 - 1/10

sinx = 3/sqrt(10)

any way we have to find sinx value so ans is 3/sqrt(10)