Find the value of tan 10 tan, 20 tan, 30 ….. tan 890.

By Ritesh|Updated : November 8th, 2022

The value of tan 10 tan, 20 tan, 30 ….. tan 890 is 1. Find the value of the given expression:

Given: tan 10 tan 20 tan 30 ….. tan 890

By solving the given expression we get,

tan 10 tan 20 tan 30 ….. tan 890 = (tan 10 tan 890) (tan 20 tan 880) ….. (tan 440 tan 460) tan 450

= (tan 10 (tan 900 - 10)) (tan 20 tan (900 - 20)) ….. (tan 440 tan (900 - 440)) tan 450

= (tan 10 cot 10) (tan 20 cot 20) ….. (tan 440 cot 440) tan 450 [tan (900 - θ) = cot θ]

= (tan 10 x 1/tan 10) (tan 20 x 1/tan 20) ….. (tan 440 x 1/tan 440) x 1 [cot θ = 1/tan θ and tan 450 = 1]

= 1 x 1 x ….. x 1

= 1

Tan Function

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.

Here is the Tangent Formula:

Tan A = Opposite Side/Adjacent side

Tangent can be modeled using sine and cosine as follows:

Tan A = Sin A / Cos A

Summary:

Find the value of tan 10 tan, 20 tan, 30 ….. tan 890.

The value of tan 10 tan 20 tan 30 ….. tan 890 is 1. Tan function in trigonometry is the ratio of the opposite to the adjacent side in a right-angled triangle. Using the trigonometric functions, it can be written as the ratio of sine to cosine.

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