Prove that `cos 20^(@) cos 40^(@) - sin5^(@) sin 25^(@) = (sqrt(3)+1)/(4)`.

Prove that cos20^(@)cos40^(@)-sin5^(@)sin25^(@)=(sqrt(3)+1)/4

cos20^(@)cos40^(@)-sin5^(@)sin25^(@)=

Prove that (i) sin 70^(@) cos 10^(@) -cos 70^(@) sin 10^(@) =(sqrt(3))/(2) (ii) cos 50^(@) cos 10^(@) -sin 50^(@) sin 10^(@) =(1)/(2) (ii) cos 80^(@) cos 20^(@) + sin 80^(@) sin 20^(@) =(1)/(2) (iv) sin 36^(@) cos 9^(@) + cos 36^(@) sin 9^(@) =(1)/(sqrt(3))

Prove that: (cos40^(@)+cos50^(@))/(sin40^(@)+sin50^(@))=1

Prove that: (cos40^(@)+cos50^(@))/(sin40^(@)+sin50^(@))=1

Prove that (sin70^(@)-cos40^(@))/(cos50^(@)-sin20^(@)) = 1/(sqrt(3)) .

Prove that : cos 130^@ cos 40^@+ sin 130^@ sin 40^@= 0 .

Prove that 8 sin20^(@) sin40^(@) sin80^(@) = sqrt3

sin20^(@)*cos40^(@)+cos20^(@)*sin40^(@)=(sqrt(3))/(2)

Prove that sin 20^(@) sin 40^(@) sin 80^(@) = (sqrt3)/(8).