Questions in trigonometry

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In triangle ABC, $A={{30}^{o}},b=8,a=6$ , then $B={{\sin }^{-1}}x$ , where $x =$
In a $\Delta ABC$ , $b=2,C={{60}^{o}},c=\sqrt{6}$ , then $a =$
In a $\Delta ABC$ , $a=5,b=4$ and $\cos (A-B)=\frac{31}{32}$ , then side c is equal to
In a $\Delta ABC$ , if $A={{30}^{o}}$ $b=2,c=\sqrt{3}+1$ , then $\frac{C-B}{2}=$
The smallest angle of the triangle whose sides are $6+\sqrt{12},\sqrt{48},\sqrt{24}$ is
If $A={{30}^{o}},c=7\sqrt{3}$ and $C={{90}^{o}}$ in $\Delta ABC$ , then $a =$
If angles of a triangle are in the ratio of $2 : 3: 7$, then the sides are in the ratio of
Sides of a triangle are $2cm,\sqrt{6}\,cm$ and $(\sqrt{3}+1)cm$. The smallest angle of the triangle is
In any triangle $ABC,\frac{\tan \frac{A}{2}-\tan \frac{B}{2}}{\tan \frac{A}{2}+\tan \frac{B}{2}}=$
If in a triangle ABC side $a=(\sqrt{3}+1)$ cms and $\angle B={{30}^{o}},$ $\angle C={{45}^{o}}$ , then the area of the triangle is

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