Здравствуйте. Всем доброго времени суток. Будьте добры подсказать формулы, которыми нужно пользоваться и как ими пользоваться на этих примерах:
1) sin(π/3 + α) + sin(π/3 - α)
2) sin²(π/4 + α) - sin²(π/4 - α)
3) cos(π/4 - β) - cos(π/4 + β)
4) cos²(α - π/4) - cos²(α + π/4)
Спасибо большое :)
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1) sin(π/3 + α) + sin(π/3 - α) = 2 sin (π/3) * cos α = V3 * cos α.
2) sin²(π/4 + α) - sin²(π/4 - α) = (sin(π/4 + α) - sin(π/4 - α)) * ( sin(π/4 + α) + sin(π/4 - α)) =
= (sin π/4 * cos α + cos π/4 *sin α - ( sin π/4 * cos α - cos π/4 *sin α)) *
* (sin π/4 * cos α + cos π/4 *sin α + ( sin π/4 * cos α - cos π/4 *sin α)) =
= ((V2 / 2) * (cos α + sin α) - (V2 / 2) * (cos α - sin α)) *
* ((V2 / 2) * (cos α + sin α)+ (V2 / 2) * (cos α - sin α)) =
= (V2 / 2) * (cos α + sin α - cos α + sin α) * (V2 / 2) * (cos α + sin α + cos α - sin α) =
= 1 / 2 * 2 sin α * cos α = sin α * cos α.
3) cos(π/4 - β) - cos(π/4 + β) = 2 cos (π/4) * cos β = V2 cos β.
4) cos²(α - π/4) - cos²(α + π/4) - аналогично п. 2.