Prove that the least positive value of `x ,` satisfying `tanx=x+1,l i e sint h ein t e r v a l(pi/4,pi/2)dot`

Prove that the least positive value of x, satisfying tan x=x+1, lies in the interval ((pi)/(4),(pi)/(2))

Prove that the least value of f(x) = (e^(x) + e^(-x)) is 2

The number of values of x satisfying cos^(2)x-cot^(2)x=1 for x in[-pi,4 pi], is

The least positive integral value of 'x' satisfying (e^(x)-2)(sin(x+(pi)/(4)))(x-log_(e)2)(sin x-cos x)<0

If m and n are the smallest positive integers satisfying the relation (2*e^(i(pi)/(6)))^(m)=(4*e^(i(pi)/(4)))^(n), then (m+n) has the value equal to

The option(s) with the values of a and L that satisfy the following equation is (are) (int_0^(4pi) e^t(sin^6 at +cos^4 at)dt)/(int_0^pi e^t (sin^6 at +cos^4 at)dt)=L

The value of l = int _(-pi//2)^(pi//2) | sin x | dx is

IfI_n=int_x^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

For any real number x ,l e t[x] denote the largest integer less than or equal to x ,L e tf be a real-valued function defined on the interval [-10 , 10] be f(x)={x-[x],if[x]i sod d1+[x]-x ,if[x]i se v e n Then the value of (pi^2)/(10)int_(-1)^(10)f(x)cospixdxi s____