Question

If α + β = 90° and `α = β/2`, then tan α tan β = ______.

Answer 1

If α + β = 90° and `α = β/2`, then tan α tan β = 1.

Explanation:

α + β = 90° and `α = β/2` 

⇒ `β/2 + β = 90^circ` 

⇒ `(3β)/2 = 90^circ` 

⇒ β = 60°

So α = 30°.

Thus tan α × tan β = tan 30° × tan 60°

= `(1/sqrt(3)) xx (sqrt(3))` 

= 1