`f(x)={2xtanx-pi/(cosx),x!=pi/2kx=pi/2i scon t inuou sa tx=pi/2,` then find the value of `kdot`

L e t f(x)=(1-tanx)/(4x-pi),x!=pi/4,x in [0,pi/2], If f(x)i s continuous in [0,pi/4], then find the value of f(pi/4)dot

If sin^(-1)(x^2+2x+2)+tan^(-1)(x^2-3x-k^2)>pi/2, then find the values of kdot

If f(x)=lambda|sinx|+lambda^2|cosx|+g(lambda) has a period = pi/2 then find the value of lambda

The area bounded by the graph of y=f(x), f(x) gt0 on [0,a] and x-axis is (a^(2))/(2)+(a)/(2) sin a +(pi)/(2) cos a then find the value of f((pi)/(2)) .

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dxdot

Draw the graph of f(x) = sec x + "cosec " x, x in (0, 2pi) - {pi//2, pi, 3pi//2} Also find the values of 'a' for which the equation sec x + "cosec " x = a has two distinct root and four distinct roots.

sin^(-1)(cosx)=(pi)/(2)-x is valid for

lim_(xto pi/2)(2x-pi)/cosx

IfI_I=int_0^(pi//2)cos(sinx)dx ,I_2=int_0^(pi/2)sin(cosx)d ,a n dI_3=int_0^(pi/2)cosx dx , then find the order in which the values I_1,I_2,I_3, exist.