Question

The biggest among $(\sin 1+\cos 1),(\sqrt{\sin 1}+\sqrt{\cos 1}),(\sin 1-\cos 1)$:

• A. $\sin 1+\cos 1$
• B. $\sqrt{\sin 1}+\sqrt{\cos 1}$
• C. $\sin 1-\cos 1$
• D. None of these

Answer 1

The correct option is B $\sqrt{\sin 1}+\sqrt{\cos 1}$

we know that if $0<x<1$ then $\sqrt{x}>x$
so $\sqrt{\sin 1}>\sin 1$ and $\sqrt{\cos 1}>\cos 1$
so $\sqrt{\sin 1}+\sqrt{\cos 1}>\sin 1+\cos 1>\sin 1-\cos 1$