Question

In a $\Delta$ ABC, right angled at C and $\angle$A = $\angle$ B,

Is $\cos A=\cos B$ ?

Answer 1

We have,

$\angle$A = $\angle$B

$\Rightarrow$ BC = AC [$\because$ Sides opposite to equal angles are equal]
$\Rightarrow$ BC = AC = x (say)
Using Pythagoras theorem in $\Delta$ ACB, we have

$A{B}^2=A{C}^2+B{C}^2$
$\Rightarrow A{B}^2=x^2+x^2$
$\Rightarrow AB=\sqrt{2x}$
(i) We have,

$cosA=\frac{AC}{AB}=\frac{x}{\sqrt{2x}}=\frac{1}{\sqrt{2}}$
$cosB=\frac{BC}{AB}=\frac{x}{\sqrt{2x}}=\frac{1}{\sqrt{2}}$

$\therefore cosA=cosB$