Maths-
General
Easy

Question

In a Δabc if b+c=3a then cot invisible function application straight B over 2 times cot invisible function application straight C over 2 has the value equal to –

  1. 4    
  2. 3    
  3. 2    
  4. 1    

Hint:

Semi perimeter of triangle = Sum of all sides, also
c o t b over 2 space equals space left parenthesis s right parenthesis open parentheses fraction numerator s minus b over denominator triangle end fraction close parentheses space a n d space c o t c over 2 space equals space space left parenthesis s right parenthesis open parentheses fraction numerator s minus c over denominator triangle end fraction close parentheses

The correct answer is: 2


     Given :In a Δabc 
    b + c = 3a
    Adding a on both sides
    a + b + c = 4a
    We know that Semi Perimeter of triangle(2S) = a +b + c
    2s = 4a
    s = 2a
    rightwards double arrow c o t b over 2 space cross times c o t c over 2 space equals space left parenthesis s right parenthesis open parentheses fraction numerator s minus b over denominator triangle end fraction close parentheses space cross times space left parenthesis s right parenthesis open parentheses fraction numerator s minus c over denominator triangle end fraction close parentheses
N o w comma space w e space k n o w space triangle squared space equals space s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis

S u b s t i t u t i n g space t h i s space v a l u e space i n space a b o v e space e q u a t i o n

rightwards double arrow c o t b over 2 space cross times c o t c over 2 space equals space fraction numerator s squared left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end fraction

rightwards double arrow c o t b over 2 space cross times c o t c over 2 space equals space fraction numerator s over denominator s minus a end fraction
s equals space 2 a comma space s u b s t i t u t i n g space t h i s space v a l u e

rightwards double arrow c o t b over 2 space cross times c o t c over 2 space equals space fraction numerator 2 a over denominator 2 a minus a end fraction space equals space space 2

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