Question

Given that sin $A=\frac{1}{2}$ and $cosB=\frac{1}{\sqrt{2}}$, then the value of (A + B) is:

• A. 75 degrees
• B. 30 degrees
• C. 15 degrees
• D. 45 degrees

Answer 1

The correct option is A

75 degrees

$sinA=\frac{1}{2}$

$\Rightarrow sinA=sin30$ $\because sin30=\frac{1}{2}$

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

and $cosB=\frac{1}{\sqrt{2}}$

$\Rightarrow cosB=cos45$ $\because cos45=\frac{1}{\sqrt{2}}$

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

Thus,$A+B={75}^{\circ }$