Find the minimum value of `alpha` where `4/sin x + 1/(1-sin x ) = alpha`

For a complex number z the minimum value of |z|+|z-cos alpha-i sin alpha| (where i=sqrt(-1)) is:

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

If (3 pi)/(4)

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

The minimum value of the expression sin alpha+sin beta+sin gamma, where alpha,beta,gamma are real numbers satisfying alpha+beta+gamma=pi is

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

Locus of the point of intersection of the lines x cos alpha+y sin alpha=a and x sin alpha-y cos alpha=b where alpha is variable.

int_ (0) ^ (pi) (xdx) / (1 + cos alpha * sin x) = (pi alpha) / (sin alpha), 0