Q63 of 76 Page 52

Fill in the blanks

If sin x + cos x = a, then


(i) sin6 x + cos6x = _______


(ii) |sin x – cos x| = ______.

Given that, sin x + cos x = a


Squaring both sides, we get


(sin x + cos x)2 = a2


⇒ sin2x + cos2x + 2sin x cos x = a2


⇒ 1 + 2sin x cos x = a2



(i) sin6 x + cos6x = (sin2x)3 + (cos2x)3


= (sin2x+ cos2x)3 -3 sin2x cos2x(sin2x+ cos2x)






(ii) |sin x – cos x| =


|sin x – cos x|2 = sin2x + cos2x - 2sin x cos x



=1-(a2 -1)


= 1-a2+1 = 2- a2


⇒ |sin x – cos x| =


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