Answer
Let's rewrite the expression on the left in terms of the ratios of sides:
$\frac{a^2}{c^2} + \frac{b^2}{c^2} = 1$
Rewrite the equation so that the fraction is combined into one:
$\frac{a^2 + b^2}{c^2} = 1$
We now look at the Pythagorean theorem, which relates the sides to the hypotenuse. The Pythagorean theorem is given by the following formula:
$a^2 + b^2 = c^2$
We can replace $a^2 + b^2$ with $c^2$:
$\frac{c^2}{c^2} = 1$
Simplify the fraction by dividing both the numerator and denominator by their greatest common factor:
$1 = 1$
The identity is verified as being true.
Work Step by Step
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