Question

Simplify : $\sin {100}^o+\cos {100}^o$

• A. $\sqrt{2}\cos 55$
• B. $\sqrt{2}\sin 55$
• C. $\sqrt{2}\sin 140$
• D. $\sqrt{2}\cos 45$

Answer 1

The correct option is A $\sqrt{2}\cos 55$

$\sin {100}^{\circ }+\cos {100}^{\circ }$

$=\sqrt{2}\{\frac{1}{\sqrt{2}}\sin {100}^{\circ }+\frac{1}{\sqrt{2}}\cos {100}^{\circ }\}$

$=\sqrt{2}\{\sin {100}^{\circ }\cos {45}^{\circ }+\cos {100}^{\circ }\sin {45}^{\circ }\}$

$=\sqrt{2}\left\{\sin {(100+45)}^{\circ }\right\}$

$=\sqrt{2}\sin {145}^{\circ }$

$=\sqrt{2}\sin (90+55{)}^{\circ }$

$=\sqrt{2}\cos {55}^{\circ }$