In a triangle ABC: ( cosA+2cosC) / (cosA+2cosB)=(sinB/sinC);?

Question

Show that the triangle is either isosceles or right angled triangle.

Answer 1

This might be tough for me to explain, since I can't draw a diagram for you.

First, draw a triangle
Secondly, label the three corners as A, B and C
Thirdly, draw a line down from A to line BC, with this point as H, and the angle AHB = AHC = 90 degrees
Fourthly, substitute all the relevant trigonometric functions with the sides.
e.g. sin C = AH/AC
cos B = BH/AB
........

Sub those expressions into the equation given in, and prove it.

Answer 2

i have tried to solve it with my calculator...
and my calculator answers...

"neither of them. show many values and I will answer for you."

i have tried to subtitute values for each.

i tried this: A = 30, B = 30, C = 120.
but it doesn't satisfy the equation.

i tried this: A = 60, B = 90, C = 30.
but it doesn't satisfy the equation also.

i have tried this: A = 45, B = 90, C = 45.
but it doesn't satisfy the equation also.

i have tried this: A = 90, B = 45, C = 45.
and it satisfy the equation.

so, i think that it works with specific values.
[or B = C to satisfy the equation.]

[its either right triangle, isosceles triangle, both (its isosceles right triangle) or not at all.]

I hope it helps.

Answer 3

If angle A is the right angle the equation holds. But not if the right angle is B or C.

If B and C are equal angles it holds. But if B and C are different and the equal angles are A and B or A and C it does not hold.