Show that `sin^2` `72^@`-`sin^2``60^@`=`(sqrt 5-1)/8`

Given that sin18^@=(sqrt5-1)/4 prove that sin^2 24^@-sin^2 6^@=(sqrt5-1)/8

Prove that sin^(2)48^(@)-cos^(2)12^(@)=-(sqrt(5)+1)/(8)

Show that 2sin^2 (pi/6)+sin^2 (pi/4)=1

Show that sin^(2)5^(@)+sin^(2)10^(@)+sin^(2)15^(@)+.....+sin^(2)90^(@)=9(1)/(2)

Show that cos ((pi)/(2)-x)=sin x

Show that sin ((pi)/(2)-x)=cos x

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

Show that (i) sin ^(2) 6 x-sin ^(2) dot(4) x=sin 2 x sin 10 x (ii) cos ^(2) 2 x-cos ^(2) 6 x=sin 4 x sin 8 x

Prove that 1-8sin^2Acos^2A=cos4A

Show that sin^-1(8/17)+sin^-1(3/5)=tan^-1(77/36)