Question

Find the value of $sin\theta +cos\theta$ when, $\theta ={45}^{\circ }.$

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

Answer 1

The correct option is B $\sqrt{2}$

When $\theta ={45}^{\circ },$
$sin\theta =\frac{1}{\sqrt{2}}$ , $cos\theta =\frac{1}{\sqrt{2}}$

So, $sin\theta +cos\theta =\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}$

Thus, $sin\theta +cos\theta =\sqrt{2}$.