3.Trigonometrical Ratios, Functions and Identities
easy

यदि $\sin A + \cos A = \sqrt 2 ,$ तो ${\cos ^2}A = $

A

$\frac{1}{4}$

B

$\frac{1}{2}$

C

$\frac{1}{{\sqrt 2 }}$

D

$\frac{3}{2}$

Solution

$\sin A + \cos A = \sqrt 2 $

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

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

Standard 11
Mathematics

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