Questions in trigonometry

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In $\Delta ABC$ , if $\tan \frac{A}{2}\tan \frac{C}{2}=\frac{1}{2},$ then $a,b,c$ are in
In triangle $ABC$ if $a,b,c$ are in A. P., then the value of $\frac{\sin \frac{A}{2}\sin \frac{C}{2}}{\sin \frac{B}{2}}=$
If $\tan \frac{B-C}{2}=x\cot \frac{A}{2},$ then $x=$
In $\Delta ABC$ , if $a=3,b=4,c=5$ , then $\sin 2B=$
If the sides of a triangle are in the ratio $2:\sqrt{6}:(\sqrt{3}+1)$ , then the largest angle of the triangle will be
In a triangle ABC, ${{a}^{3}}\cos (B-C)+{{b}^{3}}\cos (C-A)+{{c}^{3}}\cos (A-B)=$
If the lengths of the sides of a triangle be $7,4\sqrt{3}$ and $\sqrt{13}$ cm, then the smallest angle is
If the sides of a right angled triangle be in A. P. , then their ratio will be
In a $\Delta ABC$ , if $\angle C={{30}^{o}}$ , $a=47cm$ and $b=94$ cm, then the triangle is
In a $\Delta ABC$ ,side b is equal to

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