Help prove this?!

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Answer 1 · 2017-08-02T12:58:34

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

#=(sin^2theta+cos^2theta)^2-2sin^2thetacos^2theta#

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

#=1-1/4xx2sin^2 2theta#

#=1-1/4xx(1-cos4theta)#

#=1/4(4-1+cos4theta)#

#=1/4(3+cos4theta)=RHS#

Now #-1<=cos4theta <=+1#

So minimum value of

#sin^4theta+cos^4theta#

#=1/4(3-1)=1/2#

And maximum value of

#sin^4theta+cos^4theta#

#=1/4(3+1)=1#