What is the limit of (1-x) Tan (x / 2) when x approaches 1?

Tan (π X / 2) = cot (π / 2 - π X / 2) = 1 / Tan (π / 2 - π X / 2) is equivalent to 1 / (π / 2 - π X / 2)
lim[x→1] (1-x)tan(πx/2)
=lim[x→1] (1-x)/(π/2-πx/2)
=2/π
Hope to help you, if you solve the problem, please click the "select as satisfactory answer" button below

RELATED INFORMATIONS

1. How to calculate the limit of (Tan 5x) / X when x approaches 0,
2. limx->∞ x²(1-cos(2π/x)) How to calculate this? ∞-∞
3. How to find the limit of LIM (π - x) Tan (x / 2) when x → π;, How to find the limit of LIM (π - x) Tan (x / 2) when x → π
4. An advanced number problem. Derivation Y = x power + arctanx for dy / DX
5. Higher mathematics problems: on the problem of derivative What is the definition of the second derivative of F (x) at x0?
6. Two exercises on derivation of advanced numbers 1. Find the derivative dy / DX of the function y = f (x) determined by the following parametric equation (1)x=2t,y=t^2 (2)x=te^-t,y=e^t 2. Use the logarithmic derivative method to find the derivatives of the following functions (1)y=x^x Please explain the above exercises in detail, thank you~
7. High number for limit! Lim x tends to 0 (SiNx / x) ^ 1 / 2
8. A problem of finding limit in higher numbers~ Find the limit of LIM x → 1 (1-x) Tan π X / 2?
9. Failed to insert picture - = find Lim {3 / (1 ^ 2 * 2 ^ 2) + 5 / (2 ^ 2 times 3 ^ 2) + +(2n+1)/n^2*(n+1)^2}
10. Two questions about the limit of higher number 1, 1. X tends to find the limit under infinite root ((2x ^ 2) + 2x + 1) / cubic root ((8x ^ 3) - (x ^ 2) + 1) 2. X tends to infinity (((3-4x) ^ 6) ((2x-1) ^ 19)) / (5x + 1) ^ 25 to find the limit
11. Find the limit when (sin ^ 3x) / (Tan (x ^ 3)) x tends to 0 Such as the title
12. Who can analyze the trihedral angle formula? Thank you for your help
13. By analogy with the definition of equal difference and equal ratio sequence, the general term formula and summation formula of equal product sequence are derived from the definition
14. Second order arithmetic summation formula I've just been in the first grade of senior high school, and I don't know anything about it. Can you tell me the general formula for the summation of second order arithmetic? Another topic is: known, the general term formula F (n) = 12n ^ 2-12n + 3 Find f (1) + F (2) + F (3) + ＋f（500）.
15. Very basic and novice mathematical problems A * b = 144 and a = 2B
16. Rookies turn to math problems Why does equation 2 (a + 1) x ^ 2 + 4ax + 2a-1 = 0 have only one real root?
17. Excel. Number sum, the number is the text format. How to become conventional. And then sum? Text can not sum!
18. Algebraic calculation of summation formula of equal ratio sequence Formula s = A1 (1-Q ^ n) / 1-Q Suppose the sequence is 1,4,8,32128 A1 = 1, common ratio q = 4, isn't that a negative number?
19. Summation formula of second order arithmetic sequence Not the nth term
20. Sum: SN = (1 / 2) + (3 / 2 ^ 2) + (5 / 2 ^ 3) +... + [(2n-1) / 2 ^ n] It seems to be a process of seeking hope by subtracting dislocation