Question

Prove the following :
$\cos ({35}^o+A)\cdot \cos ({35}^o-B)+\sin ({35}^o+A)\cdot \sin ({35}^o-B)=\cos (A+B)$

Answer 1

L:H:S

$=cos({35}^{\circ }+A)cos({35}^{\circ }-B)+sin({35}^{\circ }+A).sin({35}^{\circ }-B)$

$=cos\left[\right({35}^{\circ }+A)-({35}^{\circ }-B\left)\right]$

$=cos(A+B)$

= R:H:S (Proved)