Question

Find the value of : $2\sin {90}^{\circ }\cos {45}^{\circ }$

• A. $\sqrt{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{\sqrt{5}}$
• D. $1$

Answer 1

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

$2\sin {90}^o\cos {45}^o=\sin ({90}^o+{45}^o)+\sin ({90}^o-{45}^o)$

$=\sin {135}^o+\sin {45}^o=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\frac{\sqrt{2}+\sqrt{2}}{2}=\sqrt{2}$