I really got trouble w/ whole lowering powers thing! need help on this one:[(cosx)^4][(sinx)^4]
$\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$
so
$\cos(2a)=\cos^2(a)-\sin^2(a)=2\cos^2(a)-1$
so
$\cos^2(a)=\dfrac{1+\cos(2a)} 2$
You can also write
$\cos(2a)=\cos^2(a)-\sin^2(a)=1-2\sin^2(a)$
so
$\sin^2(a)=\dfrac{1-\cos(2a)} 2$
and
$\cos^4(a)=\left(\dfrac{1+\cos(2a)} 2\right)^2$
$\sin^4(a)=\left(\dfrac{1-\cos(2a)} 2\right)^2$