Prove the following `4(cos^3 1 0^(@)+sin^3 2 0^(@))=3(cos1 0^(@)+sin2 0^(@))`

Prove the following identity: 4(cos^(3)10^(0)+sin^(3)20^(@))=3(cos10^(0)+sin20^(@))

Prove the following identities : (sin 0 - 2 sin^(3) 0)/ (2 cos^(3) 0 - cos 0) = tan 0

cos4 0^(@)+cos2 0^(@))=3(cos1 0^(@)+sin2 0^(@)) 40 CUSOUcos 40^@ + cos 20O 4(cos310^@ + sin320^@) = 3(cos 10^@ + sin20^@)N3.1 = 4

Prove that: (cos30^(@)+sin60^(0))/(1+cos60^(@)+sin30^(@))=(sqrt(3))/(2)

Prove tha sin 25^0 cos 115^0 = 1/2 (sin 140^0 -1)

Prove the following identity : 2 (sin^6 theta+ cos^6 theta)-3 (sin^4 theta+ cos^4 theta)+1=0 .

Prove that: sin 780^0sin 480^0+cos 120^0sin 150^0=1/2

Prove that int_0^(pi//4) cos^2 2x sin^3 4x dx=1/6

Prove that: sin(-420^0)(cos390^0)+cos(-660^0)(sin330^0)=-1.

Prove the following: 2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta)+1=0