Question

$\frac{sin(A-B)}{sinAsinB}=cotB-cotA$
If true then enter $1$ and if false then enter $0$

Answer 1

Given: $A={60}^{\circ }$ and $B={30}^{\circ }$
To Prove: $\frac{sin(A-B)}{sinAsinB}=cotB-cotA$
L.H.S: $\frac{sin(A-B)}{sinAsinB}$
= $\frac{sin({60}^0-{30}^0)}{sin{60}^{0}sin{30}^0}$
= $\frac{sin\left({30}^0\right)}{sin{60}^{0}sin{30}^0}$
= $\frac{1}{\sin {60}^0}$
= $\frac{2}{\sqrt{3}}$
R.H.S = $\cot B-\cot A$
= $\cot {30}^0-\cot {60}^0$
= $\sqrt{3}-\frac{1}{\sqrt{3}}$
= $\frac{3-1}{\sqrt{3}}=\frac{2}{\sqrt{3}}$
Thus, $L.H.S=R.H.S$