If `e^(log_^2[sin^2alpha+sin^4alpha+sin^6 alpha+…to oo])` is a root of equation `x^2-9x+8=0 where 0ltalphalt pi/2` then the principal value of `sin^-1 ((2pi)/3)` is

If sinalpha, sin^2alpha, 1 , sin^4alpha and sin^6alpha are in A.P., where -pi < alpha < pi, then alpha lies in the interval

If sin alpha=-3/6, alpha in [0,2pi] then the possible values of cos (alpha/2) , is/are

If cos (2pi)/3 =sin alpha ,which could be alpha ?

If sin alpha, sin beta and cos alpha are in GP, then roots of x^2 + 2x cot beta + 1 = 0 are always

The number of roots of the equation x^3+x^2+2x+sin x=0 in (-2pi,2pi)

If log_(sinx)(cos x) = (1)/(2) , where x in (0, (pi)/(2)) , then the value of sin x is equal to-

If sin(alpha+beta)=1 and sin(alpha-beta)=1/2 , where 0lt=alpha, betalt= pi/2 , then find the values of tan(alpha+2beta) and tan(2alpha+beta) .

If cos^4 alpha +k and sin^4 alpha+k are the roots of x^2+lambda(2 x+1)=0 and sin^2 alpha+1 and cos^2 alpha +1 are the roots of x^2 +8 x+4=0, then the sum of the possible values of lambda is

If pi/2 < alpha < 3pi /2 then the modulus argument of (1+cos 2alpha)+i sin2alpha

If sin^(4)alpha+cos^(4)beta+2=4 sin alpha cos beta, 0 le alpha, (pi)/(2) , then (sin alpha+cos beta) is equal to