Question

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

$(Here,0<A+B\le {90}^{\circ })$

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${75}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is C

${75}^{\circ }$

$Here,0<A+B\le {90}^{\circ }$

$sinA=\frac{1}{2}$ (given)

$\Rightarrow sinA=sin{30}^{\circ }$

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

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

$\Rightarrow cosB=cos{45}^{\circ }$

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

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