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  • The value of tan 1° tan 2° tan 3°… tan 89° is A. 0 B. 1 C. ½ D. Not defined

The value of \tan 1 ^{\circ} \tan 2 ^{\circ} \tan 3 ^{\circ} \ldots \tan 89 ^{\circ} \: \: \: is\\\\

A. 0

B. 1

C. 1/2

D. Not defined

Answers (1)

The answer is the option (b).    

\\\text{Given that } \tan1^{0}~\tan2^{0} \ldots \ldots \ldots \ldots \ldots .\tan89^{0}~~ \\\\ =\tan1^{0}~\tan2^{0} \ldots \ldots \tan45^{0}\tan \left( 90 - 44^{0} \right) \tan \left( 90 - 43^{0} \right) \ldots .\tan \left( 90 - 1^{0} \right) \\\\ =\tan1^{0}\cot 1^{0}\tan 2^{0}\cot 2^{0} \ldots \ldots \ldots \ldots .\tan89^{0}\cot 89^{0} \\\\ =1.1 \ldots 1 \ldots \ldots 1.1=1 \\\\

 

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