найдите сумму бесконечно геометрической прогрессии 1+sin30°+sin^2 30°+sin^3 30°+...
1-cos30°+cos^2 30°-cos^2 30°+...
1-cos30°+cos^2 30°-cos^2 30°+...
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1 + a + a^2 + ... + a^n = (1 - a^n)/(1 - a)
Пусть |a| < 1, тогда при n -> ∞ сумма -> 1/(1 - a)
1 + sin(30°) + sin^2(30°) + ... = 1/(1 - sin(30°)) = 1/(1 - 1/2) = 2
1 - cos(30°) + cos^2(30°) - ... = 1/(1 + cos(30°)) = 1/(1 + √3/2)) = (1 - √3/2)/(1 - 3/4) = 4 - 2√3