Question #b73a1
↳Redirected from
"Why is neutralization a double replacement reaction?"
# "The Reqd. Exp.="x/sqrt(1-x^2), |x| < 1.#
Recall that, #arc cos x# is defined if, &, only if, #|x| le 1.#
So, let #arc cosx=theta, and, |x| le 1.#
#:. costheta=x, and, theta in [0,pi].#
Under the substitution,
The Reqd. Exp. is, #cot theta=costheta/sintheta......(1).#
# costheta=x rArr sin^2theta=1-cos^2theta=1-x^2.#
#:. sintheta=+-sqrt(1-x^2).#
But, #theta in [0,pi], sintheta > 0. :. sintheta==sqrt(1-x^2).#
By #(1)," then, "cottheta=x/sqrt(1-x^2), x!=+-1.#
#rArr cot(arc cos x)=x/sqrt(1-x^2), |x| < 1.#
