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Show that between any two roots of tanx = 1 there exists atleast one root of tanx = –1.

Show that between any two roots of tanx = 1 there exists atleast one root of tanx = –1.

Grade:12th pass

1 Answers

Aditya Gupta
2081 Points
2 years ago
tanx = tan(pi/4)
so, x= n*pi + pi/4 where n is integer.
so, any 2 roots can be only as close as x1= m*pi + pi/4 and x2= (m+1)*pi + pi/4
now, let x3= (x1+x2)/2= (m+1/2)*pi + pi/4.= m*pi + 3pi/4
then tanx3 = tan(3pi/4)= – 1
hence, x3 is one such root. further, it lies b/w x1 and x2 as it is their avg.
kindly approve :))

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