Question

arctg(tg(-3п/5))+arcctg(ctg(-3п/5))

Answer 1

$1); ; tg(-frac{3pi}{5})=tg(-frac{3pi}{5}+pi)=tgfrac{2pi}{5}; ,; ; frac{2pi}{5}in (-frac{pi}{2};frac{pi}{2}); to \\arctg(tg(-frac{3pi}{5}))=arctg(tgfrac{2pi}{5})=frac{2pi}{5}\\2); ; ctg(-frac{3pi}{5})=ctgfrac{2pi}{5}; ,; ; frac{2pi}{5}in (-frac{pi}{2};frac{pi}{2})to \\arcctg(ctg(-frac{3pi}{5}))=arcctg(ctgfrac{2pi}{5})=frac{2pi}{5}\\3); ; arcctg(tg(-frac{3pi}{5}))+arcctg(ctg(-frac{3pi}{5}))=frac{2pi}{5}+frac{2pi}{5}=frac{4pi}{5}$