## Introduction

Tan 25 tan 110 1 tan 25 tan 110 – (find the exact value of the expression tan 25 tan 110 1 tan 25 tan 110)

In order to find the exact value of the expression tan 25 tan 110 1 tan 25 tan 110, we will need to use a few trigonometric identities. We will first start with the identity:

tan(A + B) = (tan A + tan B)/(1 – tan A * tan B)

Using this identity, we can break up the expression into two parts:

tan 25 + tan 110 = (tan25 +tan110)/(1-tan25*tan110) 1+ (-1*tan25*tan110)= (1-tan25*tan110)/(1-tan25*tan110) After we simplify each side, we will get: 2/(1-sqrt(97)) = 1+ (-1*sqrt(97))/(1-sqrt(97))

After cancelling out the common factors on each side, we are left with:

2= 1+ (-1*sqrt(97)) …

## Definition of the terms

In mathematics, the tangent is a function that describes the ratio between the length of the side opposite to an angle and the length of the side adjacent to that angle in a right-angled triangle. It is represented by the symbol tan. The function’s domain is the set of all real numbers, and its image is the set of all real numbers.

The term tangent can also refer to a line or plane that intersects a curve or surface at a point, but not necessarily at right angles. For example, a line tangent to a circle at a point on the circle’s circumference is perpendicular to the radius at that point.

## The steps to find the value

To find the value of the expression tan 25 tan 110 1 tan 25 tan 110, we will use the trigonometric identity:

tan(A+B) = (tan A + tan B)/(1 – tan A tan B)

We will plug in the values for A and B from the expression:

tan(25+110) = (tan 25 + tan 110)/(1 – tan 25 tan 110)

Now we will simplify:

(tan 25 + tan 110)/(1 – (tan 25)(tan 110)) = (0.422618261740699 + 3.38051500624656)/(1-(0.422618261740699)(3.38051500624656)) = 3.80277563773199/(-11.78620476127860) = -0.322407407407407

## The result

The result of the expression tan 25 tan 110 1 tan 25 tan 110 is -1.