5. In any triangle ABC, if atc+b+c=...
Question
Fullscreen

5. In any triangle ABC, if atc+b+c= a +8+c then show that, C= 60°.

JEE/Engineering Exams
Maths
Solution
112
Rating
4.0 (1 ratings)
Fullscreen
In sle AB ( c ) [ begin{array}{l} quad frac{1}{a+c}+frac{1}{b+c}=frac{3}{a+b+c} Rightarrow quad(a+b+c)(a+b+2 c)=3(a+c)(b+c) Rightarrow a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a+c a+b c+c^{2} Rightarrow 3 c^{2}+3 c a+3 b c+3 a b Rightarrow a^{2}+b^{2}-c^{2}-a b-a k-b c+c a+b c=0 Rightarrow a^{2}+b^{2}-c^{2}=a b frac{a^{2}+b^{2}-c^{2}}{2 a b}=frac{a b}{2 a b} end{array} ] hoe have formula for that [ begin{array}{l} cos c=frac{a^{2}+b^{2}-c^{2}}{2 a b} cos c=frac{1}{2} cos c=cos 60^{circ} end{array} ] ( C=60 )
Quick and Stepwise Solutions Just click and Send Download App OVER 20 LAKH QUESTIONS ANSWERED Download App for Free