Question

sinA +cosA=√2 find the value cos square A
$sina + cosa = \sqrt{2 \:} find \: value \: \: {cos }^{2} a$

Answer 1

Solution :

SinA + cosA = √2 -----( 1 )

Do the square ,

( sinA + cos A )² = ( √2 )²

=> sin²A+cos²A+2sinAcosA = 2

=> 1 + 2sinAcosA = 2

=> 2sinAcosA = 1

=> sin2A = sin 90°

=> 2A = 90

=> A = 90/2

=> A = 45°

Now ,

Cos²A

= cos² 45°

= ( 1/√2 )²

= 1/2

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