Evaluate: tan 26°/ tan 640°

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