(a)Show that `sin 78^@-'sin 18^@`+cos `132^@`=0.

Show that sin 3 x=3 sin x-4 sin ^(3) x

Prove that sin 600^@cos 330^@+cos 120^@sin 150^@+sin 180^@cos 180^@ = -1

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

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

Show that sin 3 x+sin 2 x-sin x=4 sin x cos (x/2) cos ((3 x)/2)

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

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

Prove that sin120^@ cos330^@ +cos240^@ sin330^@=1

Prove that cos18^(@)-sin18^(@)=sqrt(2)sin27^(@) .

Find sin 50^@cos 10^@+cos50^@sin10^@