Question

what is the value of tan inverse 2
​

Answer 1

Given:

What is the value of tan inverse 2?

To find:

Here, we need to find the value of tan ⁻2.

Solution:

To solve this we will use the Gregory series.

Gregory series:

       Gregory's series, is an infinite Taylor series expansion of the inverse tangent function. We will find the value of tan⁻1 X.

Let's see the series to fond the value of tan ⁻X.

tan⁻1 x = x - $\frac{x^{3} }{3}+\frac{x^{5} }{5}- \frac{x^{7} }{7}+\frac{x^{9} }{9}-...$

Here, we will put the value of X = 2 and find the values of series.

tan⁻1 (2) = 2 - $\frac{2^{3} }{3}+\frac{2^{5} }{5}-\frac{2^{7} }{7}+\frac{2^{9} }{9}-...$

tan⁻1 (2) = 2 - $\frac{8}{3}+\frac{32}{5}-\frac{128}{7}+\frac{512}{9}-...$

tan⁻1 (2)= 2 -2.67+6.4–18.29+56.88– ...  

tan⁻1 (2)= (2 + 6.4 + 56.88)-(2.67)  

tan⁻1 (2)= (65.28)- (2.67)

tan⁻1 (2) = 62.61

The approximate value of tan ⁻2 is 63.

Answer 2

Answer:

approx = 63⁰

Step-by-step explanation:

Solution:

To solve this we will use the Gregory series.

Gregory series:

       Gregory's series, is an infinite Taylor series expansion of the inverse tangent function. We will find the value of tan⁻1 X.

Let's see the series to fond the value of tan ⁻X.

tan⁻1 x = x - \frac{x^{3} }{3}+\frac{x^{5} }{5}- \frac{x^{7} }{7}+\frac{x^{9} }{9}-...3x3+5x5−7x7+9x9−...

Here, we will put the value of X = 2 and find the values of series.

tan⁻1 (2) = 2 - \frac{2^{3} }{3}+\frac{2^{5} }{5}-\frac{2^{7} }{7}+\frac{2^{9} }{9}-...323+525−727+929−...

tan⁻1 (2) = 2 - \frac{8}{3}+\frac{32}{5}-\frac{128}{7}+\frac{512}{9}-...38+532−7128+9512−...

tan⁻1 (2)= 2 -2.67+6.4–18.29+56.88– ...  

tan⁻1 (2)= (2 + 6.4 + 56.88)-(2.67)  

tan⁻1 (2)= (65.28)- (2.67)

tan⁻1 (2) = 62.61