দশম অধ্যায়ঃ ত্রিভুজের ধর্মাবলী

দশম অধ্যায়ঃ ত্রিভুজের ধর্মাবলী

${a \over {\sin A}} = {b \over {\sin B}} = {c \over {\sin C}} = 2R$

$\cos A = {{{b^2} + {c^2} - {a^2}} \over {2bc}}$

$\cos B = {{{c^2} + {a^2} - {b^2}} \over {2ca}}$

$\cos C = {{{a^2} + {b^2} - {c^2}} \over {2ab}}$

$a = b\cos C + c\cos B$

$b = c\cos A + a\cos C$

$c = a\cos B + b\cos A$

$\sin {A \over 2} = \sqrt {{{(s - b)(s - c)} \over {bc}}}$

$\sin {B \over 2} = \sqrt {{{(s - c)(s - a)} \over {ca}}}$

$\sin {C \over 2} = \sqrt {{{(s - a)(s - b)} \over {ab}}}$

$\cos {A \over 2} = \sqrt {{{s(s - a)} \over {bc}}}$

$\cos {B \over 2} = \sqrt {{{s(s - b)} \over {ca}}}$

$\cos {C \over 2} = \sqrt {{{s(s - c)} \over {ab}}}$

$\tan {A \over 2} = \sqrt {{{(s - b)(s - c)} \over {s(s - a)}}}  = {{(s - b)(s - c)} \over \Delta }$

$\tan {B \over 2} = \sqrt {{{(s - c)(s - a)} \over {s(s - b)}}}  = {{(s - c)(s - a)} \over \Delta }$

$\tan {C \over 2} = \sqrt {{{(s - a)(s - b)} \over {s(s - c)}}}  = {{(s - a)(s - b)} \over \Delta }$