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General

Easy

Question

The number of solution of the equation $tan invisible function application x tan invisible function application 4 x equals 1 blank$ for $0 less than x less than pi$ is

1
2
5
8

The correct answer is: 5

$tan invisible function application x tan invisible function application 4 x equals 1$
$rightwards double arrow cos invisible function application 4 x cos invisible function application x minus sin invisible function application 4 x sin invisible function application x equals 0$
$rightwards double arrow cos invisible function application 5 x equals 0$
$rightwards double arrow 5 x equals open parentheses n plus fraction numerator 1 over denominator 2 end fraction close parentheses pi comma blank n element of Z$
$rightwards double arrow x equals fraction numerator open parentheses 2 n plus 1 close parentheses over denominator 10 end fraction pi comma blank 0 less than x less than pi$
$equals fraction numerator pi over denominator 10 end fraction comma fraction numerator 3 pi over denominator 10 end fraction comma fraction numerator 5 pi over denominator 10 end fraction comma fraction numerator 7 pi over denominator 10 end fraction comma fraction numerator 9 pi over denominator 10 end fraction$
Thus, there are only five solutions

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