Question

#564
Помогите, пожалуйста

Answer 1

$sinx=frac{7}{25},; ; frac{pi}{2} textless x textless pi \\sint=frac{11}{61}; ,; ; 0 textless t textless frac{pi}{2}\\cos^2 alpha =1-sin^2 alpha ; ; to ; ; cos alpha =pm sqrt{1-sin^2 alpha }\\cosx textless 0,; t.k.; ; frac{pi}{2} textless x textless pi ; ; to ; ; cosx=-sqrt{1-frac{49}{625}}=-sqrt{frac{576}{625}}=-frac{24}{25}\\cost textgreater 0,; t.k. ; 0 textless t textless frac{pi}{2}; to ; cost=+sqrt{1-frac{121}{3721}}=sqrt{frac{3600}{3721}}=frac{60}{61}$

$sin(x+t)=sinxcdot cost+sintcdot cosx=frac{7}{25}cdot frac{60}{61} + frac{11}{61} cdot frac{-24}{25} = frac{156}{1525} \\sin(x-t)=sinxcdot cost-cosxcdot sint= frac{7}{25} cdot frac{60}{61} - frac{-24}{25} cdot frac{11}{61} = frac{264}{1525} \\cos(x+t)=cosxcdot cost-sinx cdot sint= frac{-24}{25} cdot frac{60}{61} - frac{7}{25} cdot frac{11}{61} = frac{-1517}{1525}$

 $cos(x-t)=cosxcdot cost+sinxcdot sixt= frac{-24}{25} cdot frac{60}{61} + frac{7}{25} cdot frac{11}{61} =$ $frac{-1363}{1525}$