Write the give expression in algebraic form?

Question

tan(arccos x/3)

Answer 1

When x>0 the following strategy will work:

tan(arccos(x/3))=

1) Create identities:

y = arccos(x)

x = cos(y)

2) Replace original problem with created identity:

tan(arccos(x)) = tan(y)

3) Find an identity equal to tan(y):

1 + (tan(y)^2) = (sec(y)^2)

(tan(y)^2) = (sec(y)^2) - 1

tan(y) = ((sec(y)^2) - 1)^(1/2)

4) Simplify equation by using known terms:

(sec(y)^2) = (1/(cos(y)^2)

tan(y) = ((1/(cos(y)^2) - 1)^(1/2)

(1/(cos(y)^2)) = (1/(x^2))

tan(y) = ((1/(x^2)) - 1)^(1/2)

5) Replace y with value from identity above (y = arccos(x))

tan(arccos(x)) = ((1/(x^2)) - 1)^(1/2)

6) Replace each x with (x/3)

tan(arccos(x/3)) = ((1/((x/3)^2)) - 1)^(1/2)

This is the algebraic form of tan(arccos(x/3))

Answer 2

hahah TAN.