Question

ПОМАГИТЕ СРОЧНО, РЕШИТЕ

Answer 1

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Answer 2

$1); ; (frac{sina}{tga})^2+(frac{cosa}{ctga})^2-sin^2a=cos^2a+sin^2a-sin^2a=cos^2a\\2); ; frac{tga}{sin^2a}+frac{ctga}{cos^2a}=frac{1}{sina, cosa}+frac{1}{sina, cosa}=2cdot frac{2}{sin2a}=frac{4}{sin2a}$

$3); ; frac{2sin^2a-1}{sina+cosa}=frac{-cos2a}{sqrt2cdot sin(a+frac{pi}{4})}=-frac{sqrt2, cos2a}{2cdot sin(a+frac{pi}{4})}\\ili; ; frac{2sin^2a-1}{sina+cosa}=frac{2sin^2a-cos^2a-sin^2a}{sina+cosa}=frac{sin^2a-cos^2a}{sina+cosa}=\\=frac{(sina-cosa)(sina+cosa)}{sina+cosa}=sina-cosa=\\=sqrt2cdot (frac{1}{sqrt2}cdot sina-frac{1}{sqrt2}cdot cosa)=sqrt2cdot sin(a-frac{pi }{4})\\\star ; ; tga=frac{sina}{cosa}; ; ,; ; ctga=frac{cosa}{sina} ; ; star$

$star ; ; cos2a=1-2sin^2a; ; star \\star ; ; sin2a=2, sinacdot cosa; ; star \\star ; ; sina+cosa=sqrt2cdot (frac{1}{sqrt2}cdot sina+frac{1}{sqrt2}cdot cosa)=\\=sqrt2cdot (cosfrac{pi}{4}cdot sina+sinfrac{pi }{4}cdot cosa)=sqrt2cdot sin(a+frac{pi}{4}); ; star$