Asked by Anonymous
For all real numbers x, except x = 0 and x=1, the function f is defined by f(x/(x - 1))=1/x. Suppose 0 < theta < pi / 2, What is f((sec(theta))^2)
Answers
Answered by
oobleck
if x = csc^2θ, then
x/(x-1) = csc^2θ/(csc^2θ-1) = csc^2θ/cot^2θ = sec^2θ
so I guess then that
f(sec^2θ) = csc^2θ
x/(x-1) = csc^2θ/(csc^2θ-1) = csc^2θ/cot^2θ = sec^2θ
so I guess then that
f(sec^2θ) = csc^2θ
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