Question

$ABC$ is a right isosceles triangle right angled at $B$. Then ${\sin }^{2}A+{\cos }^{2}C=$_____.

• A. $0$
• B. $\frac{1}{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $1$

Answer 1

The correct option is D $1$

As the $△ABC$ is a right isosceles with right angle at angle $B$, we have,
$\angle A={45}^0;\angle B={90}^0;\angle C={45}^0$
So, ${\sin }^{2}A+{\cos }^{2}C={\sin }^{2}45+{\cos }^{2}45=1$
Using the identity ${\sin }^{2}x+{\cos }^{2}x=1$