Answer :

Given, sin x + cos x = a


To find the value of |sin x – cos x|


Consider square of |sin x – cos x|


|sin x – cos x|2 = |sin x|2 + |cos x|2 – 2|sin x| |cos x|


[using the formula (a + b)2= a2 + b2 +2 ab]


|sin x – cos x|2 = |sin x|2 + |cos x|2 – 2|sin x| |cos x|


= (sin2 x + cos2 x)–[(sin x + cos x)2 –sin2 x –cos2 x]


= (sin2 x + cos2 x)–[a2 – (sin2 x + cos2 x) ]


[using the formula sin2 x + cos2 x = 1]


= 1 – a2 + 1


= 2 – a2


|sin x – cos x|2 = 2 – a2


Taking square root on both sides.



Hence


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