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

Thanks a lot !