Questions in trigonometry

Select	Question
	In $\Delta ABC$ , if $\angle C={{90}^{o}}$ ,$\angle A={{30}^{o}}$ , $c=20$ , then the values of a and b are
	In $\Delta ABC$ , $c\cos (A-\alpha )+a\cos (C+\alpha )=$
	In $\Delta ABC$ , $\frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=$
	In $\Delta ABC$ , ${{a}^{2}}({{\cos }^{2}}B-{{\cos }^{2}}C)+$ ${{b}^{2}}({{\cos }^{2}}C-{{\cos }^{2}}A)+$ ${{c}^{2}}({{\cos }^{2}}A-{{\cos }^{2}}B)=$
	In triangle $ABC,$ $\frac{1+\cos (A-B)\cos C}{1+\cos (A-C)\cos B}=$
	In $\Delta \,ABC$ , $\frac{\cos \frac{1}{2}(B-C)}{\sin \frac{1}{2}A}=$
	In$\Delta \,ABC$ ,$({{b}^{2}}-{{c}^{2}})\cot A+({{c}^{2}}-{{a}^{2}})\cot B+({{a}^{2}}-{{b}^{2}})\cot C=$
	If in $\Delta \,ABC$ , $2{{b}^{2}}={{a}^{2}}+{{c}^{2}},$ then $\frac{\sin 3B}{\sin B}=$
	If the sides of a triangle are in A. P., then the cotangent of its half the angles will be in
	If the angles of a triangle are in the ratio $1: 2: 3$, then their corresponding sides are in the ratio