`2^1|cosx|+|cosx|^(2 dotx)=4\ \ in\ (-pi,pi)`

If (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))=cot(a+x/2) and x in (pi,2pi) then 'a' is equal to :

Prove that tan^-1((cosx)/(1+sinx))=pi/4-x/2,\ x in (-pi/2,pi/2)

Solve (x-1)|x+1|cosx>0,forx in [-pi,pi]

Which of the following is/are correct ? (a) (tanx)^(In (cosx))lt(cotx)^(In(cosx))AAx in(pi/4,pi/2) (b) (sinx)^(In (secx))gt(cosx)^(In(cosx))AA x in(0,pi/4) (c ) (sec. pi/3)^(In (tanx))gt(sec. pi/3)^(In(cosx))AA x in (pi/4,pi/2) (d) (1/2)^(In(sinx))gt(3/4)^(In(sinx))AA x in(0,pi/2)

Number of solutions 2^(sin(|x|))=4^(|cosx|) in [-pi,pi] is equal to

If f(x)={(sin(cosx)-cosx)/((pi-2x)^2)\ \ \ ,\ \ \ x!=pi/2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \k\ \ \ \ ,\x=pi/2 is continuous at x=pi/2 , then k is equal to (a) 0 (b) 1/2 (c) 1 (d) -1

Solve |sinx+cosx|=|sinx|+|cosx|,x in [0,2pi] .

Prove that the function f(x)=cosx is strictly increasing in (pi,\ 2pi)

If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to (a) -(cosx+sinx) ,for x in (pi/4,pi/2) (b) cosx+sinx ,for x in (0,pi/4) (c) -(cosx+sinx) ,for x in (0,pi/4) (d) cosx-sinx ,for x in (pi/4,pi/2)

int_0^(pi/2) (3+4cosx)/(4+3cosx)^2dx= (A) 3/4 (B) 1/2 (C) pi/4 (D) 1/4