In the following incomplete sentences fill in the blanks such that the resulting sentences become true. If `frac{sin x}{sin y} =1/2` and `frac{cos x}{cos y}= 3/2` then `tan x = _____` and `tan y= ____`where x and y are acute angles.

In the following incomplete sentences fill in the blanks such that the resulting sentences become true. The minimum value of 27^(cos x) + 81^(sin x) is __

In the following incomplete sentences, fill in the blanks so that the resulting sentences may become true. If sin 3x ge cos 3x and 0 le x le 2pi then the solution-set of x is ______.

In the following incomplete sentences, fill in the blanks so that the resulting sentences may become true. If |tan x| lt1 and 0 le x le pi , the solution-set of x is ____.

In the following incomplete sentences fill in the blanks such that the resulting sentences become true. If tan alpha is an integral solution of the inequation 4x^(2) -16x + 15 lt 0 and cos beta is the slope of the bisector of the angle in the first quadrant between the x and y axes then the value of sin(alpha +beta)* sin(alpha - beta) =__________.

In the following incomplete sentences, fill in the blanks so that the resulting sentences may become true. For all real x, the value of sin^(2)x *cos^(2)x le k , k being the least possible. Then k= __________.

If sin x + sin y = a and cos x + cos y = b then tan ((x + y) / (2)) is

If sin x+sin y=a and cos x+cos y=b, then tan((x+y)/2 ' is equal to

If sin x + cos y = (1) / (3) and cos x + sin y = (3) / (4) then tan ((xy) / (2)) =