Question

sin (A - B) = sin A cos B - cos A sin B
If above statement is true then mention answer as 1 else mention 0 if false

Answer 1

$sin(A-B)=sinAcosB-cosAsinB$
Given, $A=B={45}^{\circ }$
Now,
L.H.S: $\sin (A-B)=\sin (45-45)=\sin 0=0$
R.H.S: $sinAcosB-cosAsinB$
= $\sin {45}^0\cos {45}^0-\cos {45}^{0}sin{45}^0$
= $\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{\sqrt{2}}\right)-\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{\sqrt{2}}\right)$
= $\frac{1}{2}-\frac{1}{2}$
= $0$
Thus, $L.H.S=R.H.S$