Questions in trigonometry

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$\frac{\sin \theta }{1-\cot \theta }+\frac{\cos \theta }{1-\tan \theta }=$
If $\tan \theta +\sec \theta ={{e}^{x}},$then $\cos \theta $ equals
If $\cos \theta -\sin \theta =\sqrt{2}\sin \theta ,$then $\cos \theta +\sin \theta $is equal to
If $\sec \theta +\tan \theta =p,$then $\tan \theta $is equal to
If $x=\sec \theta +\tan \theta ,$then $x+\frac{1}{x}=$
If $x+\frac{1}{x}=2\cos \alpha $, then ${{x}^{n}}+\frac{1}{{{x}^{n}}}=$
If $\cos \theta =\frac{1}{2}\left( x+\frac{1}{x} \right)$, then $\frac{1}{2}\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)=$
The value of ${{e}^{{{\log }_{10}}\tan 1{}^\circ +{{\log }_{10}}\tan 2{}^\circ +{{\log }_{10}}\tan 3{}^\circ +...........+{{\log }_{10}}\tan 89{}^\circ }}$ is
$\cot x-\tan x=$
$\frac{1+\sin A-\cos A}{1+\sin A+\cos A}$=

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