I cudnt solve these Question ......can u help me out plzz:- Q.1 The Smallest Positive root of the equation tan(x) - x = 0, lies in :- a) (0,pi/2) b) (pi/2, pi) c) (pi, 3pi/2) d) (3pi/2, 2pi) Q.2 The number of roots of the equation x + 2tan (x) = pi/2 in the interval [0, 2pi] is a) 1 b)2 c)3 d) infinite Thanks!

							
Dear Ashray
See the pic for the solution
 
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AKASH GOYAL
AskiitiansExpert-IIT Delhi
 
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answer to first question = as they asked about smallest positive root so tan x cant be -ve as x is always + vs nd in 0 ,pi/2 tan x is always gr8 dan x ... but from pi to 3pi/2 tan x goes from 0 to infinity  so it will at some point of time in 3rd quadrant will be = x ......... alternative method is by drawing graphs u will easily get it ............................................................................. ANSWER TO 2ND QUESTION  2TANX = PI/2 - X ........... PI/2 - X IS A STRAIGHT LINE SO U CAN DRAW IT ND THEN 2 TAN X GRAPH PLEASE DRAW IT U CAN OBSERVE THAT THE GRAPHS INTERSECTS AT 3 POSITIONS ONE EACH IN FRST 2ND ND 4TH QUADRANTS .THANK YOU PLEASE APPROVE MY ANSWER IF U LIKE IT