Question

In any $\Delta ABC$ where $\angle B={90}^{\circ }$, ${\sin }^{2}A+{\cos }^{2}C=1$

• A. True
• B. False

Answer 1

The correct option is B

False

Given that, ${\sin }^{2}A+{\cos }^{2}C=1$

But we know that ${\sin }^{2}C+{\cos }^{2}C=1$

$\therefore \text{If}si{n}^{2}A+{\cos }^{2}C=1$, then $\angle A=\angle C$

But $\angle A=\angle C$ only if $△ABC$ is isosceles.

Therefore the above statement is not always true.