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  4. Let a =5 log 5( sin x ) and b =7 log 7( cos x ) then ( a / b ) can be equal to

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Q. Let $a =5^{\log _5(\sin x )}$ and $b =7^{\log _7(\cos x )}$ then $\frac{ a }{ b }$ can be equal to

Continuity and Differentiability

Solution:

$a =5^{\log _5(\sin x)}=\sin x, \sin x>0$ and $b=7^{\log _7(\cos x)}=\cos x, \cos x>0$
$\therefore \frac{ a }{ b }=(\tan x )$, where $x \in I ^{ st }$ quadrant.