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Answer 1 · 2017-10-14T04:39:30

#LHS=sin^4t + cos^4t #

#= (cos^2t +sin^2t) ^2-2sin^2tcos^2t#

#=1^2-1/2(2sintcost)^2#

#=1-1/2(sin2t)^2#

#=1-1/2sin^2 2t#

#=1-1/4*2sin^2 2t#

#=1-1/4(1-cos4t)#

#=1-1/4+1/4cos4t#

#= 3/4 + 1/4 cos4t=RHS#