MATHEMATICAL WORLD

PROPERTIES AND SOLUTIONS OF TRIANGLE 1. SINE FORMULAE : In any triangle \(\mathrm{ABC}\) \(\dfrac{\mathrm{a}}{\sin \mathrm{A}}=\dfrac{\mathrm{b}}{\sin \mathrm{B}}=\dfrac{\mathrm{c}}{\sin \mathrm{C}}=\lambda=\dfrac{\mathrm{abc}}{2 \Delta}=2 \mathrm{R}\) where \(\mathrm{R}\) is circumradius and \(\Delta\) is area of triangle. All Chapter Notes, Concept and Important Formula 2. COSINE FORMULAE : (a) \(\mathrm{\cos A=\dfrac{b^{2}+c^{2}-a^{2}}{2 b c}}\) or \(\mathrm{a^{2}=b^{2}+c^{2}-2 b c \cos A}\) (b) \(\mathrm{\cos B=\dfrac{c^{2}+a^{2}-b^{2}}{2 c a}}\) (c) \(\mathrm{\cos C=\dfrac{a^{2}+b^{2}-c^{2}}{2 a b}}\) 3. PROJECTION FORMULAE : (a) \(b \cos C+c \cos B=a\) (b) \(c \cos A+a \cos C=b\) (c) \(a \cos B+b \cos A=c\) 4. NAPIER'S ANALOGY (TANGENT RULE) : (a) \(\tan \left(\dfrac{\mathrm{B}-\mathrm{C}}{2}\right)=\dfrac{\mathrm{b}-\mathrm{c}}{\mathrm{b}+\mathrm{c}} \cot \dfrac{\mathrm{A}}{2}\) (b) \(\tan \left(\dfrac{\mathrm{C}-\mathrm{A}}{2}\right)=\dfrac{\mathrm{c}-\mathrm{...