How to simplify (√1x2−1−1x)⋅(1−x√1−x2−1+x+√1+x√1+x−√1−x) ?

1 Answer
Shwetank Mauria
Apr 24, 2018

(√1x2−1−1x)(1−x√1−x2−1+x+√1+x√1+x−√1−x)=−1

Explanation:

Observe that √1−x2−1+x=√1−x2−(1−x)

= √1−x(√1+x−√1−x), and hence

(√1x2−1−1x)(1−x√1−x2−1+x+√1+x√1+x−√1−x)

= (√1−x2x2−1x)1−x+√1−x2√1−x(√1+x−√1−x)

= 1x(√1−x2−1)√1−x(√1−x+√1+x)√1−x(√1+x−√1−x)

= 1x(√1−x2−1)(√1−x+√1+x)(√1+x−√1−x)

= 1x(√1−x2−1)(√1−x+√1+x)2(√1+x−√1−x)(√1−x+√1+x)

= 1x(√1−x2−1)1−x+1+x+2√1−x21+x−1+x

= 1x(√1−x2−1)2+2√1−x22x

= 1x(√1−x2−1)1+√1−x2x

= 1x2(1−x2−1)

= −x2x2

= −1

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