A) undefined
B) 0
C) 1
D) 89
Correct Answer: C
Solution :
| [c] \[\tan {}^\circ \tan 2{}^\circ \tan 3{}^\circ ...\tan 89{}^\circ \] \[=\tan 1{}^\circ \tan 2{}^\circ \tan 3{}^\circ ...\tan 45{}^\circ \] \[...\tan 87{}^\circ \tan 88{}^\circ \tan 89{}^\circ \] \[=\tan 1{}^\circ \tan 2{}^\circ \tan 3{}^\circ ...\tan 45{}^\circ \] \[...\tan (90-2){}^\circ tan(90-1){}^\circ \] \[=\tan 1{}^\circ \tan 2{}^\circ \tan 3{}^\circ ...\tan 45{}^\circ ...\cot 2{}^\circ \cot 1{}^\circ \] \[=\tan 1{}^\circ \tan 2{}^\circ \tan 3{}^\circ ...\tan 45{}^\circ \] \[...\frac{1}{\tan 3{}^\circ }\frac{1}{\tan 2{}^\circ }\frac{1}{\tan 1{}^\circ }\] \[=\tan 45{}^\circ =1\] |
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