tan45

tan45 refers to the trigonometric function tangent evaluated at an angle of 45 degrees. In a right-angled triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. For an angle of 45 degrees in a right-angled triangle, the two non-hypotenuse sides are of equal length. This is because a right-angled triangle with a 45-degree angle must also have a 45-degree angle (since the sum of angles in a triangle is 180 degrees, and 180 - 90 - 45 = 45). A triangle with two equal angles is an isosceles triangle, and the sides opposite equal angles are equal in length.

Therefore, when calculating tan(45 degrees), the length of the opposite side is equal to the length of the adjacent side. This means the ratio of opposite to adjacent is length/length, which simplifies to 1. Thus, tan45 is equal to 1. This value is a fundamental constant in trigonometry and appears in various mathematical and scientific contexts, including geometry, physics, and engineering. It is a common value used in problems involving right-angled triangles and trigonometric identities.