Question

Write the value of $sin({45}^{\circ }+\theta )-cos({45}^{\circ }-\theta )$.

Answer 1

$\sin ({45}^o+\theta )-\cos ({45}^o-\theta )$

$\Rightarrow \sin 5^o\cos \theta +\cos {45}^o\sin \theta -\cos {45}^o\cos \theta -\sin {45}^o\sin \theta$

$=\frac{1}{\sqrt{2}}(\cos \theta +\sin \theta -\cos \theta -\sin \theta )$

$=0$.