Question

Намекните хотя бы, что делать в таком случае? когда пи на три плюс альфа в скобках

Answer 1

Sin(π/3 + α)=sin(π/3)·cosα + cos(π/3)·sinα
sin(π/3 - α)=sin(π/3)·cosα - cos(π/3)·sinα

₊sin²(π/3 + α)=(sin(π/3)·cosα + cos(π/3)·sinα)²
 sin²(π/3 - α)=(sin(π/3)·cosα - cos(π/3)·sinα)²
складываем:
sin²(π/3 + α)+sin²(π/3 - α)=sin²(π/3)·cos²α+2sin(π/3)·cosα ·cos(π/3)·sinα+cos²(π/3)·sin²α+
+sin²(π/3)·cos²α-2sin(π/3)·cosα ·cos(π/3)·sinα+cos²(π/3)·sin²α
упрощаем:
sin²(π/3 + α)+sin²(π/3 - α)=2sin²(π/3)·cos²α+2cos²(π/3)·sin²α
или
sin²(π/3 + α)+sin²(π/3 - α)=2(√3/2)²·cos²α+2(1/2)²·sin²α
sin²(π/3 + α)+sin²(π/3 - α)=3/2·cos²α+1/2·sin²α

Итог
sin²(π/3 + α)+sin²(π/3 - α)+sin²α=3/2·cos²α+1/2·sin²α+sin²α=3/2(cos²α+sin²α)=3/2·(1)=3/2