докажите, что (1+tga)(1+tab)=2, если a+b=п/4. Created by bonniecasper99. algebra-ru

4...

bonniecasper99 @bonniecasper99

August 2022 1 12 Report

докажите, что (1+tga)(1+tab)=2, если a+b=п/4

Answers & Comments

NNNLLL54

Verified answer

$(1+tga)(1+tgb)=1+tga+tgb+tga\cdot tgb=\\\\=1+\frac{sina}{cosa}+\frac{sinb}{cosb}+\frac{sinasinb}{cosacosb}=\frac{cosa\cdot cosb+sina\cdot cosb+sinb\cdot cosa+sina\cdot sinb}{cosa\cdot cosb}=\\\\=\frac{(cosa\cdot cosb+sina\cdot sinb)+(sinacosb+sinbcosa)}{cosa\cdot cosb}=\\\\=\frac{cos(a-b)+sin(a+b)}{\frac{1}{2}(cos(a+b)+cos(a-b))}=[\, a+b=\frac{\pi}{4},\; b=\frac{\pi}{4}-a\, ]=\\\\=\frac{cos(a-\frac{\pi}{4}+a)+sin\frac{\pi}{4}}{\frac{1}{2}(cos\frac{\pi}{4}+cos(a-\frac{\pi}{4}+a))}=$

$=\frac{2(coa(2a-\frac{\pi}{4})+\frac{\sqrt2}{2})}{\frac{\sqrt2}{2}+cos(2a-\frac{\pi}{4})}=2$

3 votes Thanks 4

bonniecasper99 огромное спасииибо

Answers & Comments

Verified answer

cherez 10 gramm smesi benzola fenola i anilina propustili tok suhogo hlorovodoro

reshit uravneniya sinx2cosx1 2sinxcosx0

pozhalujsta pomogite kak iz c2h5cl poluchit co2

uprostit vyrazhenie cos4a 6cosasinasin4a

kakaya massa hlorovodoroda proreagiruet s 15 gr amina soderzhashij massovuyu dolyu v

pri nagrevanii predelnoj alfaaminokisloty massoj 178grad vydelitsya gaz so2d4dc4d7b8a8d47b5502b26b56583867c 89504

pri nagrevanii predelnoj alfaaminokisloty massoj 178grad vydelitsya gaz so2

ukazhite 5 figur v kotorye mozhet proecirovatsya kvadrat abcd

4a

рекомендуемые вопросы

Helpful Links

Helpful Social