# Procedure for multiplying series

With power series represented as streams of coefficients as in exercise 3.59 , adding series is implemented by `add-streams` . Complete the definition of the following procedure for multiplying series:

``````(define (mul-series s1 s2)
``````

You can test your procedure by verifying that `sin²x + cos²x = 1` , using the series from exercise 3.59

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``````(define (stream-car stream) (car stream))

(define (stream-cdr stream) (force (cdr stream)))

(define (stream-map proc . list-of-stream)
(if (null? (car list-of-stream))
'()
(cons-stream
(apply proc
(map (lambda (s)
(stream-car s))
list-of-stream))
(apply stream-map
(cons proc (map (lambda (s)
(stream-cdr s))
list-of-stream))))))

(define (scale-stream stream factor)
(stream-map (lambda (x) (* x factor)) stream))

(stream-map + s1 s2))

(define (mul-streams s1 s2)
(stream-map * s1 s2))

(define (div-streams s1 s2)
(stream-map / s1 s2))

(define ones (cons-stream 1 ones))

(define integers (cons-stream 1 (add-streams ones integers)))

(define s (add-streams (mul-series sine-series sine-series)
(mul-series cosine-series cosine-series)))

(check-equal? (stream-car s) 1)``````