Cho góc nhọn a, b thỏa mãn t a n ( a ) = 1 7 , t a n ( b ) = 3 4 . Tính a + b

Do\[{\rm{0 < a, b < }}\frac{{\rm{\pi }}}{{\rm{2}}} \Rightarrow {\rm{0 < a + b < \pi }}\]

Ta có\[{\rm{tan}}\left( {{\rm{a + b}}} \right){\rm{ = }}\frac{{{\rm{tan}}\left( {\rm{a}} \right){\rm{ + tan}}\left( {\rm{b}} \right)}}{{{\rm{1}} - {\rm{tan}}\left( {\rm{a}} \right){\rm{tan}}\left( {\rm{b}} \right)}}{\rm{ = }}\frac{{\frac{{\rm{1}}}{{\rm{7}}}{\rm{ + }}\frac{{\rm{3}}}{{\rm{4}}}}}{{{\rm{1}} - \frac{{\rm{1}}}{{\rm{7}}}{\rm{.}}\frac{{\rm{3}}}{{\rm{4}}}}}{\rm{ = 1}} \Leftrightarrow {\rm{a + b = }}\frac{{\rm{\pi }}}{{\rm{4}}}\]

Đáp án cần chọn là: C