Question

simplify: tan^3(arcsec (x/2))
x= 2sec t
sqrt(x^2 -4) = 2 tan t
t = arcsec (x/2)

Answer 1

it is all in the triangle

Answer 2

there is a picture where the arc secant is x/2

Answer 3

find remaining side by pythagoras, get
\[\sqrt{x^2-4}\]

Answer 4

then find the tangent, then cube the result

Answer 5

you could also do a straight substitution
tan = sqrt(sec^2 -1)

tan = sqrt(x^2/4 -1)

tan = sqrt(x^2 -4)/2

tan^3 = (x^2-4)sqrt(x^2-4) / 8

Answer 6

so I have (x^2 -4)\[\sqrt{(x ^{2}}-4)\]

Answer 7

I get it now