Questions in trigonometry

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In $\Delta ABC,$ $1-\tan \frac{A}{2}\tan \frac{B}{2}=$
In $\Delta ABC,$ ${{b}^{2}}\cos 2A-{{a}^{2}}\cos 2B=$
In$\Delta ABC,$ a$\sin (B-C)+b\sin (C-A)+c\sin (A-B)=$
In$\Delta ABC,$ if $\cot A,\cot B,\cot C$ be in A. P., then ${{a}^{2}},\text{ }{{b}^{2}},\text{ }{{c}^{2}}$ are in
In $\Delta ABC,$ if $(a+b+c)(a-b+c)$ =3ac, then
In$\Delta ABC,$ if $2(bc\cos A+ca\cos B+ab\cos C)=$
In $\Delta ABC,$ $\text{cosec }A(\sin B\cos C+\cos B\sin C)=$
If ${{\cos }^{2}}A+{{\cos }^{2}}C={{\sin }^{2}}B,$ then $\Delta ABC$ is
If the angles of a triangle be in the ratio $1 : 2 : 7$, then the ratio of its greatest side to the least side is
If in a triangle $ABC$ , $\angle C={{60}^{o}},$ then $\frac{1}{a+c}+\frac{1}{b+c}=$

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