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  4. Value of cot 5° cot 10° ldots . . cot 85° is

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Q. Value of $\cot 5^{\circ} \cot 10^{\circ} \ldots . . \cot 85^{\circ}$ is

Trigonometric Functions

Solution:

$\cot 5^{\circ} \cot 10^{\circ} \ldots \ldots \ldots . \cot 85^{\circ}$
$=\cot 5^{\circ} \cot 10^{\circ} \ldots . \cot \left(90^{\circ}-10^{\circ}\right) \cot \left(90^{\circ}-5^{\circ}\right)$
$=\cot 5^{\circ} \cot 10^{\circ} \ldots \ldots \tan 10^{\circ} \tan 5^{\circ}$
$=\left(\tan 5^{\circ} \cot 5^{\circ}\right)\left(\tan 10^{\circ} \cot 10^{\circ}\right) \ldots \ldots . .=(1)(1)(1) \ldots \ldots .=1$