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Maths-

General

Easy

Question

If $4 n alpha equals pi comma$ then the numerical value of $tan space alpha tan space 2 alpha tan space 3 alpha horizontal ellipsis horizontal ellipsis tan space left parenthesis 2 n minus 1 right parenthesis alpha$ is equal to

-1
0
1
2

hint Hint:

In this question, we have to find the numerical value of $tan space alpha tan space 2 alpha tan space 3 alpha horizontal ellipsis horizontal ellipsis tan space left parenthesis 2 n minus 1 right parenthesis alpha$ if $4 n alpha equals pi comma$ First we will find the value of alpha, then substitute in the last values to find the simplified form of the terms. Later, put it in the in the given equation and solve to find the required numerical value.

The correct answer is: 1

$4 n minus alpha equals pi rightwards double arrow alpha equals fraction numerator pi over denominator 4 n end fraction n equals tan alpha. tan 2 alpha. tan 3 alpha....... tan left parenthesis 2 n minus 1 right parenthesis alpha A s comma space left parenthesis 2 n minus 1 right parenthesis alpha equals 2 n alpha minus alpha equals pi over 2 minus alpha tan left parenthesis 2 n minus 1 right parenthesis alpha equals tan open parentheses pi over 2 minus alpha close parentheses equals c o t space alpha tan left parenthesis 2 n minus 2 right parenthesis alpha equals tan open parentheses pi over 2 minus 2 alpha close parentheses equals c o t space 2 alpha S o comma space n equals tan alpha. tan 2 alpha. tan 3 alpha....... tan left parenthesis 2 n minus 1 right parenthesis alpha equals tan alpha. tan 2 alpha. tan 3 alpha.... c o t space 3 alpha. c o t 2 alpha. c o t alpha equals left parenthesis tan alpha. c o t alpha right parenthesis left parenthesis tan 2 alpha. c o t alpha right parenthesis left parenthesis tan 3 alpha. c o t 3 alpha right parenthesis...... equals 1.1.1.... equals 1$

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