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))`

Show that sin70^(0)cos10^(0)-cos70^(0)sin10^(0)=(sqrt(3))/(2)

Prove that (i) " sin " 80^(@) "cos " 20^(@) - " cos " 80^(@) " sin " 20^(@) =(sqrt(3))/(2) (ii) " cos " 45^(@) " cos " 15^(@) - " sin " 45^(@) " sin " 15^(@) = (1)/(2) (iii) " cos " 75^(@) " cos " 15^(@) + " sin " 75^(@) " sin " 15^(2)= (1)/(2) (iv) " sin " 40^(@) " cos " 20^(@) " + cos " 40^(@) " sin " 20^(@) =(sqrt(3))/(2) (v) " cos " 130^(@) " cos " 40^(@) l + " sin " 130^(@) " sin " 40^(@) =0

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

show that sin 55 ^(@) sin 25^(@) + cos 70^(@) .cos 10 ^(@) =( (sqrt3+1))/( 4)

Show that: cos70^(@)*cos10^(0)+sin70^(@)*sin10^(@)=(1)/(2)

Prove that sin 50^(@)-sin 70^(@)+cos 80^(@)=0 .

Prove that : sin70^@ cos 10^@- cos70^@ sin 10^@= sqrt3/2 .

Prove that sin 36 ^(@) + cos 36 ^(@) = sqrt2 cos 9^(@).

Prove that sin 36^(@) + cos 36^(@) = sqrt(2) cos 9^(@)

Prove that (sin20^(@) + sin40^(@)) + (cos20^(@) + cos40^(@))=(sqrt(3)+1)cos10^(@)