Question

The value of $10^{\log _e \cot 1^{\circ}} \cdot 10^{\log _{ e } \cot 2^{\circ}} \cdot 10^{\log _{ e } \cot 3^{\circ}} \ldots . .10^{\log _{ e } \cot 89^{\circ}}$ is equal to

• A. 0
• B. 10
• C. $\frac{1}{10}$
• D. 1

Answer 1

Answer: (D)

Given expression $=10^{\ln \cot 1^{\circ}+\ln \cot 2^{\circ}+\ldots . .+\ln \cot 89^{\circ}} $
$=10^{\ln \left(\cot 11^{\circ} \cdot \cot 2^{\circ} \cdot \cot 3^{\circ} \ldots \ldots . \cot 89^{\circ}\right)} $
$=10^{\ln \left(\cot 1^{\circ} \cdot \cot 2^{\circ} \ldots \ldots \cdot \cot \left(90^{\circ}-2\right) \cdot \cot \left(90^{\circ}-1\right)\right)}$
$=10^{\ln (1)}=10^{\circ}=1$