Question

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

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

Answer 1

Answer: (D)

$0$

Answer 2

$sin\left(45^{\circ}+\theta\right)-cos\left(45^{\circ}-\theta\right)$ $=sin45^{\circ}\,cos\theta+cos45^{\circ}sin\theta$ $-\left[cos45^{\circ}\,cos\theta+sin45^{\circ}\,sin\theta\right]$ $=\frac{1}{\sqrt{2}}cos\,\theta+\frac{1}{\sqrt{2}}sin\,\theta-\left[\frac{1}{\sqrt{2}}cos\,\theta+\frac{1}{\sqrt{2}}sin\,\theta\right]=0$