Sin2θ+cos4θ=cos2θ+sin4θ

`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`

Sum

LHS = `sin^2 theta + cos ^4 theta`

=`sin^2 theta + ( cos ^2 theta )^2`

=`sin^2 theta + (1- sin^2 theta)^2`

=` sin^2 theta + 1 -2 sin^2 theta + sin ^4 theta`

=`1-sin^2 theta + sin^4 theta`

=`cos^2 theta + sin^4 theta`

= RHS
Hence, LHS = RHS

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