A. 1- $sin^{2}$x = $cos^{2}$x
B. (1 - cosx).(1+ cosx) = 1- $cos^{2}$x = $sin^{2}$x
C.sinx - sinx.$cos^{2}$x = sinx.( 1- $cos^{2}$x ) = $sin^{3}$x
D. $sin^{4}$x + $cos^{4}$x + 2$sin^{2}$x.$cos^{2}$x + $tan{^2}$x.$cos^{2}$x
= $(sin^{2}x)^{2}$ + $(cos^{2}x)^{2}$ + 2$sin^{2}$x.$cos^{2}$x $\frac{sin^{2}x}{cos^{2}x}$.$cos^{2}$x
= 1 + $sin^{2}$x