Question

Sin^2(10°) +sin^2(50°) + sin^2(70°) = 1,5,
решить

Answer 1

sin^2(10°) +sin^2(50°) + sin^2(70°) = (1- cos(20°) + 1- cos(100°) + 1- cos(140°))/2 =

= 1,5 - 0.5( ( cos(20°) +  cos(100°) ) + cos(140°) )  =

= 1,5 - 0.5( 2сos(60°)сos(40°) + cos(180°-40°) ) = 1,5 - 0.5( сos(40°) - сos(40°) )  =

= 1.5

ЧТД