Question

If \( \sin \theta + \cos \theta = \sqrt{2} \), then what is the value of \( \theta \) (in degrees)?

• A. 30
• B. 45
• C. 60
• D. 90

Hint:

Use trigonometric identities to simplify equations involving sine and cosine sums.

Answer 1

The Correct Option is B

\[ \sin \theta + \cos \theta = \sqrt{2} \] Rewrite: 
\[ \sqrt{2} \left( \frac{\sin \theta}{\sqrt{2}} + \frac{\cos \theta}{\sqrt{2}} \right) = \sqrt{2} \Rightarrow \sqrt{2} \left( \sin \theta \cdot \frac{1}{\sqrt{2}} + \cos \theta \cdot \frac{1}{\sqrt{2}} \right) = \sqrt{2} \] \[ \sin \theta \cos 45^\circ + \cos \theta \sin 45^\circ = 1 \Rightarrow \sin(\theta + 45^\circ) = 1 \] \[ \theta + 45^\circ = 90^\circ \Rightarrow \theta = 45^\circ \] Thus, the answer is 45.