Show that `3(sinx-cosx)^(4)+6(sinx+cosx)^(2)+4(sin^(6)x+cos^(6)x)=13`

Prove that, (sinx+cosx)^2=1+sin2x

int(sinx-cosx)^(4)(sinx+cosx)dx is equal to a) (sinx-cosx)/(5)+c b) ((sinx-cosx)^(5))/(5)+c c) ((sinx-cosx)^(4))/(4)+c d) ((sinx+cosx)^(5))/(5)+c

Show that (cos x +cos y)^2 +(sinx+siny)^2=4 cos^2((x-y)/2)

int_(-pi//2)^(pi//2)sin^(2)xcos^(2)x(sinx+cosx)dx=

Show that sin 2 x=2 sin x cosx=(2 tan x)/(1+tan ^(2) x)

Prove that (sinx+sin3x)/(cosx+cos3x)=tan2x

Prove that cos^2 2x-cos^2 6x=sin4x sin8x

Prove that sin3x+sin2x-sinx=4sinxcos(x/2)cos((3x)/2)