Question

Find the value of $\sin {22}^{\circ }\cos {38}^{\circ }+\cos {22}^{\circ }\sin {38}^{\circ }$

• A. $\frac{1}{2}$
• B. $-\frac{\sqrt{3}}{2}$
• C. $\frac{\sqrt{3}}{2}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

The correct option is C $\frac{\sqrt{3}}{2}$

We know that $\sin A\cos B+\sin B\cos A=\sin (A+B)$
So, $\sin {22}^0\cos {38}^0+\sin {38}^0\cos {22}^0=\sin ({22}^0+{38}^0)=\sin {60}^0=\frac{\sqrt{3}}{2}$