Questions in trigonometry

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In a triangle $ABC$ , $\frac{2\cos A}{a}+\frac{\cos B}{b}+\frac{2\cos C}{c}=$ $\frac{a}{bc}+\frac{b}{ca}$ , then the value of angle A is
If $a=9,b=8$ and $c=x$ satisfies $3\cos C=2,$ then
If in a triangle $ABC$ , $b=\sqrt{3}$ , $c=1$ and $B-C={{90}^{o}}$ then $\angle A$ is
If in a triangle, $a{{\cos }^{2}}\frac{C}{2}+c{{\cos }^{2}}\frac{A}{2}=\frac{3b}{2},$ then its sides will be in
If in a triangle the angles are in A. P. and $b:c=\sqrt{3}:\sqrt{2}$ , then $\angle A$ is equal to
In $\Delta \,ABC$ , $a=2cm,b=3cm$ and $c=4cm$ , then angle A is
$\cot \frac{A+B}{2}$. $\tan \frac{A-B}{2}=$
If the angles $A,B,C$ of a triangle are in A.P. and the sides $a,b,c$ opposite to these angles are in G. P. then ${{a}^{2}},{{b}^{2}},{{c}^{2}}$ are in
If the sides of a triangle are p,q and$\sqrt{{{p}^{2}}+pq+{{q}^{2}}}$ , then the biggest angle is
In a triangle $ABC$ , if $B=3C$ , then the values of $\sqrt{\left( \frac{b+c}{4c} \right)}$ and $\left( \frac{b-c}{2c} \right)$ are

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