Question

If $\sin A=\frac{1}{2},\cos B=\frac{1}{\sqrt{2}}$ then the value of $(A+B)$ is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is D ${75}^{\circ }$

$\sin A=\frac{1}{2}$

$\because \sin {30}^{\circ }=\frac{1}{2}$

$\therefore A={30}^{\circ }$

$\cos B=\frac{1}{\sqrt{2}}$

$\because \cos {45}^{\circ }=\frac{1}{\sqrt{2}}$

$\therefore B={45}^{\circ }$

$\therefore (A+B)={30}^{\circ }+{45}^{\circ }={75}^{\circ }$