Відповіді АЛГЕБРА: 13.43

13.43

α = 30°

1) sin2α = sin 60° = 32

2sinα cosα = 2sin30°cos30° = 2 • 12 • 32 = 32

sin2α = 2sinα cosα

α = 60°

sin2α = sin120° = 32

2sinα cosα = 2sin60°cos60° = 2 • 32 • 12 = 32

sin2α = 2sinαcosα

2) cos²α = cos²α – sin²α

α = 30°

cos²αcos60° = 12

cos²α – sin²α = cos²30° – sin²30° = (32)² – (12)² = 34 – 14 = 12

α = 60°

cos²α = cos60°2 = cos120° = –cos60° = –12

cos²α – sin²α = cos²60° – sin²60° = 14 – 34 = –12