`2/(x-f(pi/12))+3/(x-f(pi/4))+4/(x-f((5pi)/12))=0`

Let f(x)=tan^(-1)(1/2 tan2x)+tan^(-1)(cotx)+tan^(-1)(cot^3x) then (1) f((3 pi)/8)=pi (2) f(pi/8)=0 (3) f(pi/8) =pi (4) f((3pi)/8)=0

If f(x)=(1-sin^(2)x)/(1+sin^(2)x)," then "3f'((pi)/(4))-f((pi)/(4))=

Let f:(-pi/2, pi/2)->R , f(x) ={lim_(n->oo) ((tanx)^(2n)+x^2)/(sin^2x+(tanx)^(2n)) x in 0 , n in N ; 1 if x=0 which of the following holds good? (a) f(-(pi^(-))/4)=f((pi^(+))/4) (b) f(-(pi^(-))/4)=f(-(pi^(+))/4) (c) f((pi^(-))/4)=f((pi^(+))/4) (d) f(0^(+))=f(0)=f(0^(-))

which of the following statement is // are true ? (i) f(x) =sin x is increasing in interval [(-pi)/(2),(pi)/(2)] (ii) f(x) = sin x is increasing at all point of the interval [(-pi)/(2),(pi)/(2)] (3) f(x) = sin x is increasing in interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (4) f(x)=sin x is increasing at all point of the interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (5) f(x) = sin x is increasing in intervals [(-pi)/(2),(pi)/(2)]& [(3pi)/(2),(5pi)/(2)]

which of the following statement is // are true ? (i) f(x) =sin x is increasing in interval [(-pi)/(2),(pi)/(2)] (ii) f(x) = sin x is increasing at all point of the interval [(-pi)/(2),(pi)/(2)] (3) f(x) = sin x is increasing in interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (4) f(x)=sin x is increasing at all point of the interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (5) f(x) = sin x is increasing in intervals [(-pi)/(2),(pi)/(2)]& [(3pi)/(2),(5pi)/(2)]

If f(x)=tanx and A,B,C are the anlges of /_\ABC, then |(f(A), f(pi/4) f(pi/4)), (f(pi/4), f(B) f(pi/4)), (f(pi/4), f(pi/4) f(C))| = (A) 0 (B) -2 (C) 2 (D) 1

If f(x)=tanx and A,B,C are the anlges of /_\ABC, then |(f(A), f(pi/4) f(pi/4)), (f(pi/4), f(B) f(pi/4)), (f(pi/4), f(pi/4) f(C))|= (A) 0 (B) -2 (C) 2 (D) 1

If f(x)=int_0^x("cos"(sint)+"cos"(cost)dt , then f(x+pi) is (a) f(x)+f(pi) (b) f(x)+2(pi) (c) f(x)+f(pi/2) (d) f(x)+2f(pi/2)

The domain of the function f given by f(x)=sqrt(log_(0.3)((e^(x)-1)/(e^(x)-tan x))) contains (A) (0,(pi)/(4)](B)[(pi)/(4),(pi)/(2))(C)[-(3 pi)/(4),-(pi)/(2)) (D) ((pi)/(2),(5 pi)/(4)]

If f(x) is continuous at x=(pi)/(4) where f(x)=(2sqrt(2)-(cos x+sin x)^(3))/(1-sin2x) ,for x!=(pi)/(4) then f((pi)/(4))=