Which one is true ?

Options

A. `sin1 gtsin2 gt sin3`
B. `sin1 ltsin2ltsin3`
C. `sin1lt sin3ltsin2`
D. `sin3lt sin1 ltsin2`

Answer

D

Explanation

We have,
`sin2-sin1=2sin""1/2cos""2/3gt0[because((1)/(2))^(c),((3)/(2))^(c)in(0,(pi)/(2))]`
`impliessin1ltsin2" "...(i)`
and,`sin 2-sin1=2sin1 cos 2 lt0[because2^(c)in((pi)/(2),pi)thereforecos2lt0]`
`impliessin3ltsin1" "...(ii)`
From (i) and (ii), we obtain
`sin 3 lt sin 1 lt sin2`