The value of $\frac{\tan 55^{\circ}}{\cot 35^{\circ}}+\cot 1^{\circ} \cot 2^{\circ} \cot 3^{\circ}$ $\cot 90^{\circ}$, is
(a) −2
(b) 2
(c) 1
(d) 0
We have to find the value of the following expression
$\frac{\tan 55^{\circ}}{\cot 35^{\circ}}+\cot 1^{\circ} \cot 2^{\circ} \cot 3^{\circ} \ldots \cot 90^{\circ}$
$=\frac{\tan 55^{\circ}}{\cot 35^{\circ}}+\cot 1^{\circ} \cot 2^{\circ} \cot 3 \ldots \cot 90^{\circ}$
$=\frac{\tan \left(90^{\circ}-35^{\circ}\right)}{\cot 35^{\circ}}+\cot \left(90^{\circ}-89^{\circ}\right) \cot \left(90^{\circ}-88^{\circ}\right) \cot \left(90^{\circ}-87^{\circ}\right) \ldots \cot 87 \cot 88^{\circ} \cot 89^{\circ} \ldots \cot 90^{\circ}$
$=\frac{\cot 35^{\circ}}{\cot 35^{\circ}}+\tan 89^{\circ} \tan 88^{\circ} \tan 87^{\circ} \ldots \cot 87 \cot 88^{\circ} \cot 89^{\circ} \ldots \cot 90^{\circ}$
$=1+1 \times 1 \times 1 \ldots \times 0$
$=1$
As $\cot 90^{\circ}=0$
Hence the correct option is $(c)$
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