Question

If $A={60}^{\circ }$ and $B={30}^{\circ }$, Write the values of $\cos A,\cos B$ and $\cos (A+B)$.

Is $\cos (A+B)=\cos A+\cos B?$

Answer 1

If $A={60}^o$, $B={30}^o$

$\cos \left(A\right)\Rightarrow \cos {60}^o=\frac{1}{2}$

$\cos \left(B\right)\Rightarrow \cos \left({30}^o\right)=\frac{\sqrt{3}}{2}$

$\cos (A+B)=\cos A\cos B-\sin A\sin B$

$\cos \left(90\right)=\left(\frac{1}{2}\right)\left(\frac{\sqrt{3}}{2}\right)-\left(\frac{\sqrt{3}}{2}\right)\left(\frac{1}{2}\right)=0$

$\cos (A+B)\ne \cos A+\cos B$.