MCQ
Choose the correct answer from the given four options. $\sin(45^\circ+\theta)-\cos(45^\circ-\theta)$ is equal to :
- A$2\cos\theta$
- ✓$0$
- C$2\sin\theta$
- D$1$
✓
Answer
Correct option: B.
$0$
$\sin(45^\circ+\theta)-\cos(45^\circ-\theta)$
$=\cos[90^\circ-(45^\circ+\theta)]-\cos(45^\circ-6)$
$[\therefore\cos(90^\circ-\theta)=\sin0]$
$=\cos(45^\circ-0)-\cos(45^\circ-0)$
$=0$
$=\cos[90^\circ-(45^\circ+\theta)]-\cos(45^\circ-6)$
$[\therefore\cos(90^\circ-\theta)=\sin0]$
$=\cos(45^\circ-0)-\cos(45^\circ-0)$
$=0$
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