Q. 8cos^3(20) - 8sin^3(10) - 6cos20 + 6sin10 = 2

Soln:

L.H.S.

= 8cos³20 – 8sin³10 – 6cos20 + 6sin10

= 2(4cos³20 – 4sinn³10 – 3cos20 + 3sin10)

= 2(4cos³20 - 3cos20 + 3sin10 – 4sin³10)

= 2(cos3.20 + sin3.10)   [∵ cos3A = 4cos³A – 3cosA and sin3A = 3sinA – 4sin³A]

= 2(cos60 + sin30)

= 2(1/2 + 1/2)

= 2