Question

State True/False

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.