If A + A = 2 , then ^2 A = - Vidyadip

MCQ

If $\sin A + \cos A = \sqrt 2 ,$ then ${\cos ^2}A = $

A
$\frac{1}{4}$
✓
$\frac{1}{2}$
C
$\frac{1}{{\sqrt 2 }}$
D
$\frac{3}{2}$

✓

Answer

Correct option: B.

$\frac{1}{2}$

b
(b) $\sin A + \cos A = \sqrt 2 $.

On squaring both the sides

==> $1 + \sin 2A = 2\, \Rightarrow \sin 2A = 1 = \sin {90^o}$

==> $2A = {90^o}$ or $A = {45^o}$

Now, ${\cos ^2}A = {(\cos {45^o})^2} $

$= {\left( {\frac{1}{{\sqrt 2 }}} \right)^2} = \frac{1}{2}$.

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