Question

Solve for x:

[sin^-1(cos^-1(sin^-1(tan^-1x)))] = 1 where [,] = GIF

Answer 1

Given, [sin^-1(cos^-1(sin^-1(tan^-1x)))] = 1

⇒ 1 ≤ sin^-1(cos^-1(sin^-1(tan^-1x))) < 2

⇒ sin(1) ≤ cos^-1(sin^-1(tan^-1x)) , sin(2)

⇒ cos(sin(2)) < sin^-1(tan^-1x) ≤ cos(sin(11))

⇒ sin(cos(sin(2))) < (tan^-1x) ≤ sin(cos(sin(1)))

⇒ tan(sin(cos(sin(2)))) < x ≤ tan(sin(cos(sin(1))))