Question
यदि $\sin A + \cos A = \sqrt 2 ,$ तो ${\cos ^2}A = $
दोनों तरफ वर्ग करने पर,
$\Rightarrow 1 + \sin 2A = 2\, \Rightarrow \sin 2A = 1 = \sin {90^o}$
$\Rightarrow 2A = {90^o}$या $A = {45^o}$
अब ${\cos ^2}A = {(\cos {45^o})^2}$
$= {\left( {\frac{1}{{\sqrt 2 }}} \right)^2} = \frac{1}{2}$.
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$(A)$ $\int_0^1 x \cos x d x \geq \frac{3}{8}$ $(B)$ $\int_0^1 x \sin x d x \geq \frac{3}{10}$ $(C)$ $\int_0^1 x^2 \cos x d x \geq \frac{1}{2}$ $(D)$ $\int_0^1 x^2 \sin x d x \geq \frac{2}{9}$