The point D divides the side AB of the triangle ABC internally in the ratio of m:n . If angle ACD =a , angle BCD = b , and angle BDC = \theta , use the sine rule to show taht

$\displaystyle \frac{AD}{sin a}=\frac{DC}{sin(\theta-a)}$

$\displaystyle \frac{BD}{sin b }=\frac{DC}{sin(\theta+b)}$

I can show this part . The one below is what i am not sure of .

Hence , prove that $\displaystyle (m+n)\cot \theta=m\cot a-n\cos b$