Question

Find the value of: tan10, tan20,………..tan450,…………tan890

Answer 1

SOLUTION

TO DETERMINE

The value of

$\sf{ \tan {10}^{ \circ}. \tan {20}^{ \circ}. \: ... \:\tan {450}^{ \circ} \: \: .. \:\tan {890}^{ \circ} }$

EVALUATION

We have to find the value of

$\sf{ \tan {10}^{ \circ}. \tan {20}^{ \circ}. \: ... \:\tan {450}^{ \circ} \: \: .. \:\tan {890}^{ \circ} }$

So the given expression

$\sf{ = \tan {10}^{ \circ}. \tan {20}^{ \circ}. \: ... \:\tan {450}^{ \circ} \: \: .. \:\tan {890}^{ \circ} }$

$\sf{ \tan {10}^{ \circ}. \tan {20}^{ \circ}. \: .\tan {360}^{ \circ}.. \:\tan {450}^{ \circ} \: \: .. \:\tan {890}^{ \circ} }$

Now

$\sf{\tan {360}^{ \circ} }$

$\sf{ = \tan (4 \times {90}^{ \circ} + {0}^{ \circ} ) }$

$\sf{ =\tan {0}^{ \circ} }$

$\sf{ =0}$

Therefore

$\sf{ \tan {10}^{ \circ}. \tan {20}^{ \circ}. \: ... \:\tan {450}^{ \circ} \: \: .. \:\tan {890}^{ \circ} }$

$\sf{ = \tan {10}^{ \circ}. \tan {20}^{ \circ}. \: .\tan {360}^{ \circ}.. \:\tan {450}^{ \circ} \: \: .. \:\tan {890}^{ \circ} }$

$\sf{ = 0 }$

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