how to simplify sums having power of 4 or its multiples such as... simplify- sin^4T+cos^4T

the given quantity=(sin^2x+cos^2x)^2-2sin^2xcos^2x

=1-sin^2(2x)/2to simplify trig functions one must need lots of practice

Write it as:
=(sin^2T+cos^2T)^2 - 2(sin^2T.cos^2T)
hence,
= 1 - (sin2T)^2/2

cos^4t+sin^4t=(sin^2+cos^2)^2-2sin^2t.cos^2t
=1-sin^2 2t
      _______   ANS
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use the formulae a^2+b^2= (a+b)^2- 2ab

then puting a=sin^2x and b=cos^2x we the ans

which is 1- 2(sinx.cosx)^2