A) \[\cot \,\frac{B}{2}\]
B) \[\tan \,\frac{A}{2}\]
C) \[\cot \,\frac{C}{2}\]
D) \[\cot \,\frac{A}{2}\]
Correct Answer: B
Solution :
We know that, \[A+B+C=180{}^\circ \] \[\Rightarrow A=180{}^\circ -\left( B+C \right)\Rightarrow \frac{A}{2}=\frac{1}{2}\left[ 180{}^\circ -\left( B+C \right) \right]\]\[\Rightarrow \frac{B+C}{2}=90{}^\circ -\frac{A}{2}\] \[\Rightarrow \,\,\tan \left( \frac{B+C}{2} \right)=\tan \,\left[ 90{}^\circ -\frac{A}{2} \right]\] [take both sides tan] \[\Rightarrow \,\,\tan \,\left( \frac{B+C}{2} \right)=\cot \,\frac{A}{2}\]
You need to login to perform this action.
You will be redirected in
3 sec
