Question

The value of $\sin(45^{\circ} + \theta) - \cos(45^{\circ} - \theta)$ is:

• A. 0
• B. $2\sin\theta$
• C. $\sqrt{2}\cos\theta$
• D. 1

Hint:

$45^{\circ} + \theta$ and $45^{\circ} - \theta$ are complementary angles as their sum is $90^{\circ}$.

Answer 1

The Correct Option is A

Step 1: Concept
Use the complementary angle identity $\sin(A) = \cos(90^{\circ}-A)$.
Step 2: Analysis
$\sin(45^{\circ} + \theta) = \cos(90^{\circ} - (45^{\circ} + \theta)) = \cos(45^{\circ} - \theta)$.
Step 3: Conclusion
The expression becomes $\cos(45^{\circ} - \theta) - \cos(45^{\circ} - \theta) = 0$.
Final Answer: (A)