What is sqrt(1-x^2)*sqrt(1+(x^2)/(1-x^2)) ?

The solution to sqrt(1-x^2)*sqrt(1+(x^2)/(1-x^2)) is 1

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simplify sqrt(1-x^2)*sqrt(1+(x^2)/(1-x^2))

simplify

1 - x^{2} \cdot 1 + \frac{x ^{2}}{1 - x ^{2}}

1

Solution steps

1 - x^{2} 1 + \frac{x ^{2}}{1 - x ^{2}}

Apply radical rule:

a b = a \cdot b

- x^{2} + 1 \frac{x ^{2}}{- x ^{2} + 1} + 1 = (- x^{2} + 1) (\frac{x ^{2}}{- x ^{2} + 1} + 1)

= (- x^{2} + 1) (\frac{x ^{2}}{- x ^{2} + 1} + 1)

(1 - x^{2}) (1 + \frac{x ^{2}}{1 - x ^{2}}) = 1

= 1

Apply rule

1 = 1

= 1

(\frac{π}{2})^{2}

- 2 (0.7639) e^{- (0.7639)^{2}}

What is sqrt(1-x^2)*sqrt(1+(x^2)/(1-x^2)) ?
The solution to sqrt(1-x^2)*sqrt(1+(x^2)/(1-x^2)) is 1