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  4. If w= log sin 1 cos 1, x= log sin 1 tan 1, y= log cos 1 sin 1 and z= log cos tan 1 then

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Q. If $w=\log _{\sin 1} \cos 1, x=\log _{\sin 1} \tan 1, y=\log _{\cos 1}$ $\sin 1$ and $z=\log _{\cos } \tan 1$ then

Trigonometric Functions

Solution:

Since $\frac{\pi}{4}<1, \cos 1<\sin 1<1<\tan 1$
Hence $\log _{\sin 1} \tan 1<\log _{\cos 1} \tan 1<0$
$0<\log _{\cos 1} \sin 1<\log _{\cos 1} \cos 1=1$
and $1=\log _{\sin 1} \sin 1<\log _{\sin 1} \cos 1$
$\therefore x < z < y < w$