Questions in trigonometry

Select	Question
	The value of $\cos A-\sin A$when $A=\frac{5\pi }{4},$ is
	The value of $\cos (270{}^\circ +\theta )\,\cos (90{}^\circ -\theta )-\sin (270{}^\circ -\theta )\,\cos \theta $ is
	If $\cos (\alpha -\beta )=1$ and $\cos (\alpha +\beta )=\frac{1}{e}$, $-\pi <\alpha ,\beta <\pi $, then total number of ordered pair of $(\alpha ,\beta )$ is
	If $\sin A=\frac{1}{\sqrt{10}}$and $\sin B=\frac{1}{\sqrt{5}},$where A and B are positive acute angles, then $A+B=$
	If $\tan A=2\tan B+\cot B,$then $2\tan (A-B)=$
	If $\sin A+\sin B=C,\cos A+\cos B=D,$then the value of $\sin (A+B)=$
	If $\sin A=\sin B$and $\cos A=\cos B,$then
	$\sin 50{}^\circ -\sin 70{}^\circ +\sin 10{}^\circ =$
	${{\cos }^{2}}48{}^\circ -{{\sin }^{2}}12{}^\circ =$
	If $y=(1+\tan A)(1-\tan B)$ where $A-B=\frac{\pi }{4}$, then ${{(y+1)}^{y+1}}$ is equal to