Question

Evaluate \(2(\sin 45^\circ - \cos 45^\circ)\).

• A. \(0\)
• B. \(1\)
• C. \(2\)
• D. \(-2\)

Hint:

For \(45^\circ\), sine and cosine are equal, so any difference like \(\sin 45^\circ - \cos 45^\circ\) vanishes to zero.

Answer 1

The Correct Option is A

Step 1: Recall exact values of \(\sin 45^\circ\) and \(\cos 45^\circ\).
We know \(\sin 45^\circ = \dfrac{1}{\sqrt{2}}\), \(\cos 45^\circ = \dfrac{1}{\sqrt{2}}\).
Step 2: Substitute into the expression.
\[ 2(\sin 45^\circ - \cos 45^\circ) = 2\left(\dfrac{1}{\sqrt{2}} - \dfrac{1}{\sqrt{2}}\right) = 2(0) = 0. \]
Step 3: Conclude.
Therefore, the value is \(0\).