Simplify evaluate if possible b cos2cos1rad32 c tansec12 d c

Simplify (evaluate) if possible:

b) cos(2cos^-1(rad3/2))

c) tan(sec^-1(2))

d) cot(csc^-1(3))

e) sin(cos^-1(5/2))

f) tan(tan^-1(5/2))

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

let sin^-1 (1/ sqrt 2) = x

sin x = 1/ sqrt 2

therefore,

sin ( x) = 1/ sqrt 2

= sqrt 2 / 2

b) cos ( 2 cos^-1 ( sqrt 3 /2 ))

let cos^-1 ( sqrt 3 /2 ) = x

cos x = sqrt 3 / 2

sin x = 1 / 2

hence , cos ( 2x ) = cos^2 x - sin^2 x = ( sqrt 3 / 2)^2 - (1/2)^2

= 3 / 4 - 1/4 = 1/ 2

c) tan ( sec^-1 (2) )

let sec^-1 (2) = x

sec x = 2

therefore, tan x = sqrt 3

d) cot (csc^-1(3))

let csc^-1 (3) = x

csc x = 3

therefore, cot x = sqrt 8