If `alpha in [-2pi, 2pi]` and `cos.(alpha)/(2)+sin.(alpha)/(2)=sqrt(2)(cos 36^(@)-sin18^(@))`, then a value of `alpha`

cos((alpha)/(2))+sin((alpha)/(2))=sqrt(2)(cos36^(@)-sin18^(@))

If (pi)/(2)ltalphalt(2pi)/(3)andl=int_(0)^(sin2alpha)(dx)/(sqrt(4cos^(2)alpha-x^(2))) , then the value of (l+alpha)/(pi) must be__________.

If (pi)/(2)ltalphalt(2pi)/(3)andl=int_(0)^(sin2alpha)(dx)/(sqrt(4cos^(2)alpha-x^(2))) , then the value of (l+alpha)/(pi) must be__________.

If cos alpha + cos beta =cos ""(3pi)/(7)and sin alpha + sin beta = sin ""(3pi)/(7), then the value of cos ^(2)""(alpha-beta)/(2) is-

If 0 lt alpha lt (pi)/(2) and sin alpha + cos alpha = sqrt2, then the value of cos 3 alpha is-

If |(sin^(2)alpha,cos^(2)alpha),(cos^(2)alpha,sin^(2)alpha)|=0,alphain(0,pi) , then the values of alpha are

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=