Question

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

• A. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. ${30}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is A ${45}^{\circ }$

Trigonometric angles for some specific cosine acute angles are given below,

$\begin{array}{cccccc}\theta & 0^{\circ }& {30}^{\circ }& {45}^{\circ }& {60}^{\circ }& {90}^{\circ }\\ cos\theta & 1& \frac{\sqrt{3}}{2}& \frac{1}{\sqrt{2}}& \frac{1}{2}& 0\end{array}$

From the above table we can see that $A+B={45}^{\circ }$