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2015-06-19T15:01:40+05:30

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Phase difference between the two waves = 90°
addition of amplitudes follows vector sum rule 
so the resultant will be = √(A² + A² + 2AAcos90)
                                  = √(2A²)
                                  = A√2 
 
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2015-06-20T15:28:51+05:30

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Acos(wt) = Asin(90+wt) 
Therefore phase difference = 90
Since the frequency is same
Resultant Vector is =  \sqrt{ A^{2} + A^{2} } = A \sqrt{2} sin(wt)
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