Question

If ΔABC is an isosceles right triangle right angled at B, then `(tan A + cot C)/(cot A + cot C)` = ______.

Answer 1

If ΔABC is an isosceles right triangle right angled at B, then `(tan A + cot C)/(cot A + cot C)` = 1.

Explanation:

In an isosceles right triangle with right angle at B, the other two angles are equal and together sum to 90°, so A = C = 45°.

Thus tan A = tan 45° = 1 and cot A = cot 45° = 1 (same for C).

So `(tan A + cot C)/(cot A + cot C) = (1 + 1)/(1 + 1)`

= `2/2`

= 1