Questions in trigonometry

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	In any triangle ABC, the value of $a({{b}^{2}}+{{c}^{2}})\cos A+b({{c}^{2}}+{{a}^{2}})\cos B+c({{a}^{2}}+{{b}^{2}})\cos C$ is
	In a triangle $ABC$ , $AD$ is altitude from A. Given $b>c,$ $\angle C={{23}^{o}}$ and $AD=\frac{abc}{{{b}^{2}}-{{c}^{2}}},$ then $\angle B=$
	If $A={{60}^{o}}$ , $a=5,b=4\sqrt{3}$ in $\Delta ABC$ , then $B =$
	If $\Delta ={{a}^{2}}-{{(b-c)}^{2}}$ , where $\Delta $ is the area of triangle $ABC$ , then tan A is equal to
	If ${{c}^{2}}={{a}^{2}}+{{b}^{2}}$ , then $4s(s-a)(s-b)(s-c)=$
	If ${{p}_{1}},{{p}_{2}},{{p}_{3}}$ are altitudes of a triangle $ABC$ from the vertices $A,B,C$ and $\Delta $ the area of the triangle, then $p_{1}^{-2}+p_{2}^{-2}+p_{3}^{-2}$ is equal to
	If the median of $\Delta ABC$ through A is perpendicular to $AB$ , then
	If A is the area and 2s the sum of 3 sides of triangle, then
	If in a triangle $ABC$ right angled at $B,s-a=3$ , $s-c=2$ , then the values of a and c are respectively
	In triangle ABC and DEF, AB = DE, AC = EF and $\angle A=2\angle E$. Two triangles will have the same area, if angle A is equal to