A) 1-sin^x B) (1-cosx)(1+cosx) C) sinx-sinx.cos^x D) sin4x+cos4x+2sin^x.cos^x+tan^x.cos^x

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