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  • Użytkownik Zadane
2013-07-15T12:44:28+02:00

a=sin⁴α - cos⁴α  = (sin²α - cos²α)(sin²α + cos²α) = (sin²α - cos²α) * 1  = sin²α - cos²α = (sin60*)² - (cos60*)² = (√3/2)² - (1/2)² = 3/4 - 1/4 = 2/4 = 1/2


b=1-4sin²αcos²α = 1 - ( 2 * sinα * cosα)² = 1 - (2 * sin60* * cos60*)² = 1 - (2 * √3/2 * 1/2)² = 1 - (√3/2)² = 1 - 3/4 = 1/4

 

a - b = 1/2 - 1/4 = 2/4 - 1/4 = 1/4    -------  odpowiedź

2013-07-15T13:26:27+02:00

α = 60°

sin60° = √3/2

cos60° = ½

 

a = sin⁴α - cos⁴β = (sin60°)² - (cos60°)⁴ = (√3/2)⁴ - (½)⁴ = 9/16 - 1/16 = 8/16 = 1/2

 

b = 1 - 4sin²αcos²α = 1 - 4(sin60°)²·(cos60°)² = 1 - 4(√3/2)²·(1/2)² = 1 - 4 · 3/4 · 1/4 = 1 - 3/4 = 1/4

 

a - b = 1/2 - 1/4 = 2/4 - 1/4 = 1/4

a - b = 1/4

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