Grade 12th passTrigonometry

in a traingle ABC find the value of ∑tanb/2 . tanc/2

manjit

10 Years agoGrade 12th pass

1 Answer

BALAJI ANDALAMALA

10 Years ago

In a triangle ABC , A+B+C=180
$\frac{A+B+C}{2}=90$
Take Tan on both sides ,we get
$tan(\frac{A}{2}+\frac{B}{2}) = tan(90-\frac{C}{2}) = cot\frac{C}{2}$
Apply the formula tan(x+y) = (tanx+tany)/(1-tanxtany) ,we get
$\Rightarrow \frac{tan\frac{A}{2}+tan\frac{B}{2}}{1-tan\frac{A}{2}tan\frac{B}{2}} =cot\frac{C}{2}$
$\Rightarrow tan\frac{A}{2}tan\frac{C}{2}+tan\frac{B}{2}tan\frac{C}{2}={1-tan\frac{A}{2}tan\frac{B}{2}}$
$\therefore tan\frac{A}{2}tan\frac{C}{2}+tan\frac{B}{2}tan\frac{C}{2} +tan\frac{A}{2}tan\frac{B}{2} =1$