Write the trigonometric expression as an algebraic expressio

Write the trigonometric expression as an algebraic expression in u cos (tan u cos (tan-1)- (Type an exact answer, using radicals as needed.)

Solution

cos(tan^-1u)

tan^-1u= x

tan x =u/1

opposite=u, adjacent=1

hypotenuse=sqrt(1+u²)

cos x= adjacent / hypoteuse

cos x= 1/sqrt(1+u²)

cos(tan^-1u) =1/sqrt(1+u²)