Let `alpha` be a solution of `tan x+sin2x=sec x` and `alpha in[-2 pi,2 pi]` ,then

Statement -1 the solution of the equation (sin x)/(cos x + cos 2x)=0 is x=n pi, n in I Statement -2 : The solution of the equation sin x = sin alpha , alpha in [(-pi)/(2),(pi)/(2)] x={npi+(-1)^(n)alpha,n in I}

If Tan theta= Tan alpha then general solution is theta= , when alpha in((-pi)/(2),(pi)/(2))

Number of solutions of the equation 2tan^(2)x-5sec x=1 in (-pi,2 pi) is equal to

If alpha

Let alpha=pi/3 then the solution set of the inequality log _sinalpha (2-cos^2x) ltlog_sin alpha (1-sinx) where xepsilon (0,2pi) and x!=pi/2

If tan x cot y= sec alpha where alpha is constant and alpha in (-(pi)/(2), (pi)/(2))then (d ^(2)y)/(dx ^(2))at ((pi)/(4), (pi)/(4)) equal to:

Number ofintegral solutions of the equation |tan x+sec x|=|tan x|+|sec x| in [0,2 pi] is

If tan alpha =2 and 0 lt alpha lt (pi)/(2) then prove that x =a, pi +alpha are the solution of the equation (tan(2alpha-x))/(tan (2alpha+x))=11 that lies between 0 and 2pi

Let f:[0,2] to RR be the function defined by f(x)=(3-sin (2pix)) sin (pi x-(pi)/(4)) - sin (3pi x+(pi)/(4)) If alpha,beta in [0,2] are such that {x in [0,2]: f(x) ge0}= [alpha, beta] , then the value of beta- alpha is._________

If the quadratic polynomial y=(cot alpha)x^(2)+2(sqrt(sin alpha))x+(1)/(2)tan alpha,alpha in[0,2 pi] can take negative values for all x in R, if alpha in((5 pi)/(lambda),pi), then the value of lambda is