In a $\Delta ABC,$ if $A:B:C = 3:5:4,$ then $a + b + c\sqrt{2}$ is equal to

In triangle $ABC$,if $a=4, b=3, c=2$,then $2(a-b \cos C)(a-c \sec B) = $

In a $\triangle ABC$,if $\frac{a}{b^2-c^2} + \frac{c}{b^2-a^2} = 0$,then $B$ is equal to

In $\triangle ABC$,$a^2 \sin 2B + b^2 \sin 2A =$

If $7$ and $8$ are the lengths of two sides of a triangle and '$a$' is the length of its smallest side. The angles of the triangle are in $AP$ and '$a$' has two values $a_1$ and $a_2$ satisfying this condition. If $a_1 < a_2$ then $2 a_1 + 3 a_2 =$

In a $\triangle ABC$,the sides $a, b, c$ are in $A$.$P$. if and only if $r_1, r_2, r_3$ are in