# Evaluate: tan 26°/ tan 640°

By BYJU'S Exam Prep

Updated on: September 25th, 2023

tan 260/ tan 640 is 1.

The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle. One of the six fundamental functions in trigonometry is the tangent function.

### Tangent Formula

Tan A = Opposite Side/Adjacent side

Tangent can be modelled using sine and cosine as follows:

Tan A = Sin A / Cos A

We are aware that an angle’s cosine is equal to the ratio of the length of the adjacent side to the length of the hypotenuse side, whereas an angle’s sine is equal to the length of the opposite side divided by the length of the hypotenuse side.

To evaluate tan 260/ tan 640

We can write 260 as 260 = (900 – 640)

So tan 260 = tan (900 – 640)

tan 260 = cot 640 [As tan (900 – θ) = cot θ]

Now replacing the value of tan 260 from the above we get

tan 260/ tan 640 = cot 720/ cot 720

On simplifying we get

tan 260/ tan 640 = 1

Summary:-

## Evaluate: tan 26°/ tan 640°

tan 260/ tan 640 is 1. The tan value is obtained by calculating the ratio of adjacent side length to the opposite side length.

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