Помогите доказать тождества. Created by Koteno4ek2017. algebra-ru

Помогите доказать тождества...

Koteno4ek2017 @Koteno4ek2017

October 2021 1 11 Report

Помогите доказать тождества

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a) Sin⁴α + 2Sin²αCos²α + Cos⁴α + Sin²α + Cos²α =

= (Sin⁴α + 2Sin²ααCos² + Cos⁴α) + (Sin²α + Cos²α) =

= (Sin²α + Cos²α)² + (Sin²α + Cos²α) = 1² + 1 = 2

2 = 2

Тождество доказано

б)

$Sin(\alpha+\frac{\pi }{3})-Sin(\alpha-\frac{\pi }{3})= 2Sin\frac{\alpha+\frac{\pi }{3}-\alpha+\frac{\pi }{3}}{2}Cos\frac{\alpha+\frac{\pi }{3}+\alpha-\frac{\pi }{3}}{2}=2Sin\frac{\pi }{3} Cos\alpha=2*\frac{\sqrt{3} }{2}Cos\alpha=\sqrt{3}Cos\alpha\\\\\sqrt{3}Cos\alpha=\sqrt{3}Cos\alpha$

Тождество доказано

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