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)

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