If A,B,C are the angles of a triangle such that angle A is obtuse, then tanBtanC will be less than13√3√21none of these.

The given question is about the properties of a triangle. In a triangle, the sum of all angles is 180 degrees. If angle A is obtuse, it means it is greater than 90 degrees. Let's assume angle A = 90 + x (where x is the acute angle).

So, the sum of angles B and C would be 90 - x (since the sum of all angles in a triangle is 180 degrees).

Now, we know that tan(90 - x) = cot(x). So, tanBtanC = tan(90 - x)tan(90 - x) = cot(x)cot(x) = 1/tan^2(x).

Since x is an acute angle, tan^2(x) will always be greater than 1. Therefore, 1/tan^2(x) will always be less than 1.

So, tanBtanC will be less than 1. Hence, the correct answer is "less than 1".