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  4. The value of sin(45°+θ)-cos(45°-θ) is

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

Trigonometric Functions

Solution:

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