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  • The value of (tan1° tan2° tan3° ... tan89°) is (A) 0 (B) 1 (C) 2 (D) 1 by 2

The value of (tan1° tan2° tan3° ... tan89°) is
(A) 0                (B) 1                (C) 2                (D)1/2

Answers (1)

Answer.          [B]                  
Solution.         Given :-tan1° tan2° tan3° ... tan89°
tan1° tan2° tan3° ... tan89°tan87° tan 88° tan89°       …(1)
We can also write equation (1) in the form of
[tan (900 – 890) . tan (900 – 880). tan (900 – 870) …… tan 87° . tan 88° tan 89°]
[\because we can write tan 1° in the form of tan (900 – 890) similarly we can write other values]
[cot 890 . cot 880. cot 870 …. tan 870 . tan 880 . tan 890]
\because   [tan (902 – \theta) = cot\theta ]

Also

\left [ \frac{1}{\tan 89^{\circ}}\frac{1}{\tan 88^{\circ}} \frac{1}{\tan 87^{\circ}}\cdots \tan 87^{\circ}.\tan 88^{\circ}\tan 89^{\circ} \right ]

\because Throughout all terms are cancelled by each other and remaining will be tan45

Hence the value is 1

 \because option B is correct.

Posted by

infoexpert27

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