Question

what is::

$tan25°tan15° + tan15°tan50° + tan25°tan50°$=?
​

Answer 1

Answer:

Since, there are 3 angles involved, let us assume:

A = 15 deg.

B = 25 deg.

C = 50 deg.

The most important thing to note is that, here, A + B + C = 90 deg.

Using the trigonometric formula:

On the Left-Hand Side (L.H.S.), we have tan(90 deg.) which tends to infinity. This means that the denominator of the Right-Hand Side (R.H.S.) has to be zero i.e.:

1 - tan(A)*tan(B) - tan(B)*tan(C) - tan(C)*tan(A) = 0.

On substituting the values of A, B and C, we get the proof for your question:

tan(15)*tan(25) + tan(25)*tan(50) + tan(50)*tan(15) = 1

[all angles are in degrees]

Step-by-step explanation:

★__Hope this will help you__★