If `(4*alpha)/(alpha^2+1)>=1` and ` alpha +1/alpha` is an odd integer then number of possible values of `alpha` is

if int_(alpha)^( alpha+1)(dx)/((x+alpha)(x+alpha+1))=log_(e)((9)/(8)) then number of values of alpha is

If lim_(x to alpha) (alpha^x - x^alpha)/(x^alpha - alpha^alpha) = -1 then what is the value of alpha ?

If (2 sin alpha)/(1 + cos alpha + sin alpha) = 3/4 , then the value of (1 + cos alpha + sinalpha)/(1 + sin alpha) is equal to

If (2 sin alpha)/(1 + cos alpha + sin alpha) = 3/4 , then the value of (1 - cos alpha + sinalpha)/(1 + sin alpha) is equal to

If sin^(2)alpha+ sin alpha=1 , then the value of cos^(4) alpha+ cos^(2) alpha is ________

For a real number alpha , let A(alpha) denote the matrix ((cosalpha,sinalpha),(-sinalpha,cosalpha)) . Then for real numbers alpha_(1) and alpha_(2) , the value of A(alpha_(1))A(alpha_(2)) is -

If |{:(1+x^(2),3x,x+1),(5,x,x^(3)),(0,1,x+2):}|=(alpha_(1)-x)(alpha_(2)-x)(alpha_(3)-x)(alpha_(4)-x)(alpha_(5)-x) is an identity, where alpha_(1),alpha_(2),alpha_(3),alpha_(4),alpha_(5) are complex numbers independent of x ,then the value of alpha_(1)*alpha_(2)*alpha_(3)*alpha_(4)*alpha_(5) is

If alpha is a complex number such that alpha^(2)+alpha+1=0 , then the value of alpha^(61) is

If a variable takes the discrete value alpha+4alpha-(7)/(2),alpha-(5)/(2),a-3,alpha-2,alpha+(1)/(2),alpha-(1)/(2)alpha+5(alpha>0), then the median of these values:

If 2(sin alpha)/(1+cos alpha+sin alpha)=y then value of (1-cos alpha+sin alpha)/(1+sin alpha) is