Given `alpha` lies in `IV` quadrant and `sin(alpha)/(2)+cos(alpha)/(2)=(-1)/(2),` if `sin2 alpha=(-a sqrt(7))/(b),` then `a+b` is equal to

If 0 < alpha < pi/6 and sin alpha + cos alpha =sqrt(7 )/2, then tan alpha/2 is equal to

if (tanalpha-i(sin ""(alpha)/(2)+cos ""(alpha)/(2)))/(1+2 i sin ""(alpha)/(2)) is purely imaginary then alpha is given by -

If alpha and beta be between 0 and (pi)/(2)and if cos(alpha+beta)=(12)/(13) and sin(alpha-beta)=3/5, then sin 2 alpha is equal to

If alpha is an acute angle and sin(alpha/2)=sqrt((x-1)/(2x)) then tan alpha is

The value of expression (tan alpha+sin alpha)/(2"cos"^(2)(alpha)/(2)) for alpha=(pi)/(4) is :

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

If sin alpha + sin beta=a and cos alpha+cosbeta=b then tan((alpha-beta)/2) is equal to

If 0ltalpha,betaltpi and cos alpha+cos beta -cos(alpha+beta)=(3)/(2) , then the value of sqrt3 sin alpha+cos alpha is equal to

The value of (sin(pi-alpha))/(sin alpha-cos alpha tan.(alpha)/(2))-cos alpha is

If the eccentric angles of the extremities of a focal chord of an ellipse x^2/a^2 + y^2/b^2 = 1 are alpha and beta , then (A) e = (cos alpha + cos beta)/(cos (alpha + beta)) (B) e= (sin alpha + sin beta)/(sin(alpha + beta)) (C) cos((alpha-beta)/(2)) = e cos ((alpha + beta)/(2)) (D) tan alpha/2.tan beta/2 = (e-1)/(e+1)