Question

prove the identity ( sin 6 teta + cos 6 teta) = 1 - 3sin 2 teta cos 2 teta

Answer 1

split sin6 nd cos6 into (sin2)3+(cos2)3= use identity a3+b3 = (a+b)(a2+b2-ab) here a=sin2 b=Cos2 put this in identity u will get (sin2+cos2)((sin2)2+(cos2)2-sin2 cos2 )= (1)(sin4+cos4-sin2cos2) then add nd subtract 2sin2cos2= sin4+ cos4 -2sin2cos2+2sin2cos2 - sin2cos2 = (sin2+ cos2)2-3 sin2 cos2= 1-3sin2 cos2