let f(a) = ∫_0 ^(π/2) (dx/(1+asinx)) with a∈R
1) find a simple form of f(a)
2) calculate ∫_0 ^(π/2) (dx/(1+sinx)) and ∫_0 ^(π/2) (dx/(1+2sinx))
3) find the value of ∫_0 ^(π/2) ((cosx)/((1+asinx)^2 ))dx
4) find the value of ∫_0 ^(π/2) ((cosx)/((1+sinx)^2 ))dx and ∫_0 ^(π/2) ((cosx)/((1+2sinx)^2 ))dx
If α, β are the roots of the equation
ax^2 +bx+c=0, then the value of the
determinant
determinant ((1,(cos (β−α)),(cos α)),((cos (α−β)),1,(cos β)),((cos α),(cos β),1)) is