(i) sin2 A+ cos4 A = cos2 A+ sin4 A
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sin4A+cos4A
We have (a2+b2)2=a4+b4+2a2b2
⇒a4+b4=(a2+b2)2−2a2b2
Take a=sinA and b=cosA we get
sin4A+cos4A=(sin2A+cos2A)2−2sin2Acos2A
=1−2sin2Acos2A proved.
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