How to do both the questions?

Dear Student ,

6.
$$\begin{gathered} \tan 1\times \tan 2\times \tan 3\times .........\times \tan 89=\tan 1\times \tan 2\times \tan 3\times ....\times \tan 44\times \tan 45\times \tan 46\times .....\times \tan 88\times \tan 89 \\ =\tan 1\times \tan 2\times \tan 3\times ....\times \tan 44\times \tan 45\times \tan \left(90-44\right)\times .....\times \tan \left(90-2\right)\times \tan \left(90-1\right) \\ =\tan 1\times \tan 2\times \tan 3\times ....\times \tan 44\times \tan 45\times \cot 44\times .....\times \cot 2\times \cot 1 \left(\tan \left(90-\mathrm{\theta }\right)=\mathrm{cot\theta }\right) \\ =\tan 1\times \tan 2\times \tan 3\times ....\times \tan 44\times \tan 45\times \frac{1}{\tan 44}\times .....\times \frac{1}{\tan 2}\times \frac{1}{\tan 1} \left(\mathrm{cot\theta }=\frac{1}{\mathrm{tan\theta }}\right) \\ =\tan 45 \\ =1 \\ \mathrm{Hence}, \mathbf{tan}\mathbf{1}\mathbf{\times }\mathbf{tan}\mathbf{2}\mathbf{\times }\mathbf{tan}\mathbf{3}\mathbf{\times }\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{\times }\mathbf{tan}\mathbf{89}\mathbf{=}\mathbf{1} \\ \mathbf{Option}\mathbf{ }\mathbf{\left(}\mathbf{B}\mathbf{\right)}\mathbf{ }\mathbf{is}\mathbf{ }\mathbf{correct}\mathbf{.} \end{gathered}$$

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