Question

Prove that: $\sin {105}^o+\cos {105}^o=\frac{1}{\sqrt{2}}$

Answer 1

$\sin {105}^{\circ }+\cos {105}^{\circ }$

$=\sin 75-\sin 15$

$=2\sin \left(\frac{75-15}{2}\right)\cos \left(\frac{75+15}{2}\right)$

$=2\left(\frac{1}{2}\right)\left(\frac{1}{\sqrt{2}}\right)=\frac{1}{\sqrt{2}}$