Prove that `4(cos ^(3) 10^(@) + sin ^(3) 20^(@)) = 3 ( cos 10^(@) + sin 20^(@)).`

i) Prove that: cos^(3)2A+3cos2A = 4(cos^(6)A-sin^(6)A) ii) Prove that: 4(cos^(3)10^(@) + sin^(3)20^(@)) = 3(cos10^(@)+sin20^(@))

4 (cos ^(3) 20^(@) + cos ^(3) 40^(@)) = 3 ( cos 20 ^(@) + cos 40^(@))

What is the value of (cos 10 ^(@) + sin 20^(@))/( cos 20^(@) - sin 10 ^(@))?

Prove that (cos ^(3) A - sin ^(3) A)/( cos A - sin A ) = (2 + sin 2 A)/( 2 ).

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

Prove that : 4(sin^(4)30^(@)+cos^(4)60^(@))-3(cos^(2)45^(@)-sin^(2)90^(@))=2

Prove that : 4(sin^(4)30^(@)+cos^(4)60^(@))-3(cos^(2)45^(@)-sin^(2)90^(@))=2

Prove that : (cos^(3) A + sin^(3) A)/ (cos A + sin A) + (cos^(3) A - sin^(3) A)/(cos A - sin A) = 2

(1)/(sin 10^(@)) - (sqrt3)/(cos 10 ^(@)) = 4.

Prove that : (i) sin42^(@)cos48^(@)+sin48^(@)cos42^(@)=1 (ii) cos70^(@)cos20^(@)-sin70^(@)sin20^(@)=0