Question

$cos(A+B)=cosAcosB-sinAsinB$
If above statement is true then mention 1 as answer else mention 0 for false.

Answer 1

$cos(A+B)=cosAcosB-sinAsinB$
Given, $A=B={45}^{\circ }$
Now,
L.H.S: $\cos (A+B)=\cos ({45}^0+{45}^0)=\cos {90}^0=0$
R.H.S: $cosAcosB-sinAsinB$
= $\cos {45}^0\cos {45}^0-\sin {45}^0\sin {45}^0$
= $\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{\sqrt{2}}\right)-\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{\sqrt{2}}\right)$
= $\frac{1}{2}-\frac{1}{2}$
= $0$
Thus, $L.H.S=R.H.S$