Question

If $m=4,n=6$ and $k\cot \theta =p\cot B+q\cot C$, then find the value of $k+p+q$.

Answer 1

To find: $k+p+q$

By $m-n$ cot theorem:

$m+n\cot \theta =n\cot B-m\cot C$

$4+6\cot \theta =6\cot B-4\cot C$

$10\cot \theta =6\cot B-4\cot C$

$k+p+q=10+6-4=12$

Here we get the answer if we consider $k,p,q$ as in $m-ntheorem$ but if we consider some multiple such as $2$ on both sides answers may be different.