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. $f ( x )< g ( x )< h ( x ) \forall x \in\left(\frac{\pi}{2}, \pi\right)$
• B. $f(x)=g(x)=h(x) \forall x \in\left(\frac{\pi}{4}, \frac{\pi}{3}\right)$
• C. $h(x)>g(x)>f(x) \forall x \in\left(\frac{3 \pi}{2}, 2 \pi\right)$
• D. $ f(x)>g(x)$ has no real solution

Answer 1

Answer: (B), (C), (D)