trig-substitute.sls

#!r6rs

(library (mpl trig-substitute)

  (export trig-substitute)

  (import (mpl rnrs-sans)
          (mpl match)
          (mpl arithmetic)
          (mpl sin)
          (mpl cos))

  (define (trig-substitute u)
    (if (or (number? u)
            (symbol? u))
        u
        (let ((v (map trig-substitute u)))
          (match v
            (('tan x) (/ (sin x) (cos x)))
            (('cot x) (/ (cos x) (sin x)))
            (('sec x) (/ 1 (cos x)))
            (('csc x) (/ 1 (sin x)))
            (else v)))))

  )