prove that f(x)= 2 tan^-1(x) + sin^-1 { 2x/1+x^2} is a constant for all x>or= 1. find that constant?

Asked by pspratimasingh588 | 16th Aug, 2010, 10:38: PM

Expert Answer:

f(x) = 2tan-1(x) + sin-1 { 2x/1+x2}
Put x = tan θ
f(tan θ) = 2tan-1(tan θ) + sin-1 { 2tan θ/1+tan2 θ}
f(tan θ) = 2tan-1(tan θ) + sin-1 { 2tan θ/sec2 θ}
f(tan θ) = 2tan-1(tan θ) + sin-1 { 2sin θ cos θ}
f(tan θ) = 2θ + sin-1 { sin 2θ }
f(tan θ) = 2θ + 2θ
f(tan θ) = 4θ
Now x = tan θ > = 1
θ = π/4 for x = 1,
so the constant is 4θ = π.
Regards,
Team,
TopperLearning.

Answered by  | 17th Aug, 2010, 10:44: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.