Question

What is the value of \( \sin 45^\circ + \tan 45^\circ \)?

• A. \( \frac{\sqrt{2}-1}{\sqrt{2}} \)
• B. \( \frac{2-\sqrt{2}}{2} \)
• C. \( \frac{\sqrt{2}+1}{\sqrt{2}} \)
• D. None of these

Hint:

For standard angles like \( 45^\circ \), remember that \( \sin 45^\circ = \tan 45^\circ = \frac{1}{\sqrt{2}} \), which simplifies calculations significantly.

Answer 1

The Correct Option is C

We know that: \[ \sin 45^\circ = \frac{1}{\sqrt{2}} \quad \text{and} \quad \tan 45^\circ = 1 \] So: \[ \sin 45^\circ + \tan 45^\circ = \frac{1}{\sqrt{2}} + 1 \] \[ = \frac{1 + \sqrt{2}}{\sqrt{2}} \] Thus, the correct answer is \( \frac{\sqrt{2}+1}{\sqrt{2}} \).