Fill in the blanks so that the following statements are correct.
The larger of $cos log θ$ and $log cos θ$ if $e^{- π / 2} < θ < π / 2$ is......

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Solution

Ans. $cos log θ$ .
For $e^{- π / 2} < θ < π / 2$ , we have
$- \frac{π}{2} < log θ < log \frac{π}{2}$
Now ${log}_{e} e = 1, \frac{π}{2} < e ∴ log \frac{π}{2} < log e = 1$
$∴ - \frac{π}{2} < log θ < 1 \frac{π}{2}$
Above shows that $log θ$ lies in $1$ st or $4$ st quadrant.
$∴ cos (log θ) = +$ ive, i.e. $> 0$ $(1)$
Now $0 < cos θ < 1 ∴ log cos θ < log 1 = 0$
$∴ log cos θ = -$ ive, i.e. $< 0$ $(2)$
From $(1)$ and $(2)$ , we conclude that
$cos log θ > log cos θ$ .

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