Question

A) cos84° × cos54° + sin84° × sin54° =
b) sin105°=

Answer 1

$\cos84^\circ\cos54^\circ+\sin84^\circ\sin54^\circ=\cos(84^\circ-54^\circ)=\cos30^\circ=\dfrac{\sqrt{3} }{2}$

$\sin105^\circ=\sin(60^\circ+45^\circ)=\sin60^\circ\cos45^\circ+\cos60^\circ\sin45^\circ=$

$=\dfrac{\sqrt{3} }{2} \cdot\dfrac{\sqrt{2} }{2}+\dfrac{1 }{2} \cdot\dfrac{\sqrt{2} }{2}=\dfrac{\sqrt{6}}{4}+\dfrac{\sqrt{2} }{4}=\dfrac{\sqrt{6}+\sqrt{2} }{4}$