$\sin $^{2}$ x $ `=` $\dfrac{1-cos(2x)}{2}$

$\sin $^{4}$ x $ `=` $\dfrac{3-4cos(2x) + cos (4x)}{8}$

$\cos $ $^{2}$ `=`$\dfrac{3+4cos(2x) + cos(4x)}{8}$