Answer
True
Work Step by Step
$Sin^{2}α=(\frac{Opposite Side Of \angleα}{Hypotenuse})^{2}=\frac{a^{2}}{c^{2}}$
$Cos^{2}α=(\frac{Adjacent Side Of \angleα}{Hypotenuse})^{2}=\frac{b^{2}}{c^{2}}$
Now, Adding the two values, we get: $\frac{a^{2}}{c^{2}}+\frac{b^{2}}{c^{2}}=\frac{a^{2}+b^{2}}{c^{2}}$
By Pythagorean Theorem we know: $a^{2}+b^{2}=c^{2}$
Substituting $c^{2}$ in the previous equation, we get: $\frac{a^{2}+b^{2}}{c^{2}}=\frac{c^{2}}{c^{2}}$
$\frac{c^{2}}{c^{2}}=1$
Therefore, $Sin^{2}α+Cos^{2}α=1$
