Find the value of `sin2alpha` when

If sin alpha=(4)/(5) , then find the value of sin 2 alpha .

Find the value of sin 2 alpha, if sin alpha+ cos alpha=(1)/(3) .

Find the value of (sin (alpha + beta))/(sin (alpha - beta)), "given that" tan alpha = 2 tan beta.

If alpha , beta are complementry angles such that bsin alpha = a , the find the value of (sin alpha cos beta - cos alpha sin beta) .

If "tan" alpha=-2 , find the value of "sin" alpha ( alpha lies in the II Quadrant).

Find the value of sin^6 alpha+ cos^6 alpha+ 2sin^2 alpha cos^2 alpha .

If sin(alpha+beta)=(4)/(5), sin(alpha-beta)=(5)/(13) , find the value of tan 2alpha :