If angle C of triangle ABC is `90^0,` then prove that `tanA+tanB=(c^2)/(a b)` (where, `a , b , c ,` are sides opposite to angles `A , B , C ,` respectively).

If A+B=90^(@) then prove that 1+(tanA)/(tanB)=sec^(2)A.

If in a triangle A B C ,/_C=60^0, then prove that 1/(a+c)+1/(b+c)=3/(a+b+c) .

Using vectors , prove that in a triangle ABC a/(sin A) = b/(sin B) = c/(sin C) where a,b,c are lengths of the ideas opposite to the angles A,B,C of triangle ABC respectively .

Using vectors , prove that in a triangle ABC a^(2)= b^(2) + c^(2) - 2bc cos A where a,b,c are lengths of the ideas opposite to the angles A,B,C of triangle ABC respectively .

Let ABC is be a fixed triangle and P be veriable point in the plane of triangle ABC. Suppose a,b,c are lengths of sides BC,CA,AB opposite to angles A,B,C, respectively. If a(PA)^(2) +b(PB)^(2)+c(PC)^(2) is minimum, then point P with respect to DeltaABC is

In an acute angled triangle ABC, prove that tan^(2)a+tan^(2)B+tan^(2) C ge9 .

Using vectors , prove that in a triangle ABC a = b cos C + c cos B where a,b,c are lengths of the ideas opposite to the angles A,B,C of triangle ABC respectively .

If an a triangle A B C , a=3b and B-A=90^0, then find the value of tanA

If an a triangle A B C , b=3 c, a n d C-B=90^0, then find the value of tanB

If in a triangle ABC, (a-b+c)/2 = ab/(b+c-a) then prove that angleC=90^(@) .