Вопрос от посетителя:
Доказать :
1)(tgα+ctgα)²-(tgα-ctgα)²=4
2)(2+sinα)(2-sinα)+(2+cosα)(2-cosα)=7
3)ctgα+sinα/1+cosα=1/sinα
4)1-2sinαcosα/sinα-cosα=sinα-cosα
решите пожалуйста )
Илюха отвечает:
1)(tgα+ctgα)²-(tgα-ctgα)²= (tg²α + 2 * tg α * ctg α + ctg²α) – (tg²α – 2 * tg α * ctg α + ctg²α) = 4 * tg α * ctg α = 4
2) (2+sinα) * (2-sinα) + (2+cosα) * (2-cosα)= 4 – sin²α + 4 – cos²α = 8 – (sin²α + cos²α) = 8 – 1 = 7
3) ctgα + sinα/(1+cosα) = cosα/sinα + sinα/(1+cosα) = (cosα*(1 + cosα) + sinα*sinα)/(sinα *(1 + cosα)) = (cos²α + cosα + sin²α)/(sinα * (1 + cosα) = 1/sinα
4) (1 – 2*sinα*cosα)/(sinα-cosα) = (1 – 2*sinα*cosα)/(sinα-cosα) = (sin²α – 2*sinα*cosα + cos²α)/(sinα – cosα) = (sinα – cosα)² / (sinα – cosα) = sinα-cosα