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Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
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The value of $\tan 1^{\large\circ}\tan 2^{\large\circ}\tan 3^{\large\circ}$........$\tan 89^{\large\circ}$ is

$\begin{array}{1 1}(A)\;0&(B)\;1\\(C)\;\large\frac{1}{2}&(D)\;\text{Not defined}\end{array} $

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1 Answer

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Toolbox:
  • $\cot \theta.\tan\theta=1$
  • $\tan(\large\frac{\pi}{2}$$-\theta)=\cot \theta$
$\tan 1^{\large\circ}\tan 2^{\large\circ}\tan 3^{\large\circ}$.......$\tan 89^{\large\circ}$
$\tan(90^{\large\circ}-89^{\large\circ})\tan(90^{\large\circ}-88^{\large\circ})\tan (90^{\large\circ}-87^{\large\circ})........\tan 45^{\large\circ},\tan 46^{\large\circ}$.......$\tan 89^{\large\circ}$
$\cot 89^{\large\circ}\cot 88^{\large\circ}\cot 87^{\large\circ}$........$\tan 45^{\large\circ},\tan 46^{\large\circ}$......$\tan 89^{\large\circ}$
$\Rightarrow 1$
Hence (B) is the correct answer.
answered Apr 21, 2014 by sreemathi.v
 
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