(1): cos ∠A = (2√2)/3
cos ∠B = cos 2∠A
cos 2∠A = cos (∠A+∠A)
= cos∠Acos∠A-sin∠Asin∠A
= cos²∠A - sin²∠A
= 8/9 - 1/9 = 7/9
(2): ∠C = 180°-∠A-∠B = 180°-3∠A
sin ∠C = sin ( 180°-3∠A ) = sin 3∠A
sin 3∠A = 3sin∠A - 4sin³∠A = 3(1/3) - 4(1/3)³
= 1 - 4(1/27) = 1 - 4/27 = 23/27 |
