Question #77e3a

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Answer 1 · 2016-12-21T05:44:50

#LHS=2sin^6x+2cos^6x+1#

#=2((sin^2x)^3+(cos^2x)^3+1#

#=2((sin^2+cos^2x)^3-3sin^2xcos^2x(sin^2x+cos^2x)+1#

#=2*(1)^3-3*2*sin^2xcos^2x*(1)+1#

#=3-3*2*sin^2xcos^2x#

#=3(1^2-2*sin^2xcos^2x)#

#=3((sin^2x+cos^2x)^2-2*sin^2xcos^2x)#

#=3((sin^2x)^2+(cos^2x))^2#

#=3(sin^4x+cos^4x)#

#=3sin^4x+3cos^4x=RHS#

Proved