If f(x)= sin -1( sin x), g(x)= cos -1( cos x) and h(x)= cot -1( cot x) then which of the following is (are) correct?

Question

If f(x)= sin -1( sin x), g(x)= cos -1( cos x) and h(x)= cot -1( cot x) then which of the following is (are) correct? (A) f ( x )< g ( x )< h ( x ) ∀ x ∈((π/2), π) (B) f(x)=g(x)=h(x) ∀ x ∈((π/4), (π/3)) (C) h(x)>g(x)>f(x) ∀ x ∈((3 π/2), 2 π) (D) f(x)>g(x) has no real solution

Tardigrade Admin · Accepted Answer

Q. If $f (x) = sin^{- 1} (sin x), g (x) = cos^{- 1} (cos x)$ and $h (x) = cot^{- 1} (cot x)$ then which of the following is (are) correct?

$f (x) < g (x) < h (x) \forall x \in (\frac{π}{2}, π)$

$f (x) = g (x) = h (x) \forall x \in (\frac{π}{4}, \frac{π}{3})$

$h (x) > g (x) > f (x) \forall x \in (\frac{3 π}{2}, 2 π)$

$f (x) > g (x)$ has no real solution

Q. If f(x)=sin−1(sinx),g(x)=cos−1(cosx) and h(x)=cot−1(cotx) then which of the following is (are) correct?

f(x)<g(x)<h(x)∀x∈(2π​,π)

f(x)=g(x)=h(x)∀x∈(4π​,3π​)

h(x)>g(x)>f(x)∀x∈(23π​,2π)

f(x)>g(x) has no real solution

Q. If $f (x) = sin^{- 1} (sin x), g (x) = cos^{- 1} (cos x)$ and $h (x) = cot^{- 1} (cot x)$ then which of the following is (are) correct?

$f (x) < g (x) < h (x) \forall x \in (\frac{π}{2}, π)$

$f (x) = g (x) = h (x) \forall x \in (\frac{π}{4}, \frac{π}{3})$

$h (x) > g (x) > f (x) \forall x \in (\frac{3 π}{2}, 2 π)$

$f (x) > g (x)$ has no real solution