In the following incomplete sentences fill in the blanks such that the resulting sentences become true. If `sin 17^circ *sin 43^circ *sin 77^circ = lambda sin 51^circ` then `lambda` is equal to

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 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. 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. 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 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 each of the following,fill in the blank so that the resulting sentence becomes true. intdx/(1+x^2)^(3//2) =______.

In the following incomplete sentences fill in the blanks such that the resulting sentences become true. Let cos 3x = 4cos x* cos(x +beta)* cos(x - beta) , 0 lt beta lt pi/2 Then the value of 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= __________.

In each of the following,fill in the blank so that the resulting sentence becomes true. int(x^2+x+2)/((1+x^2)(1+x))dx =_____.

Prove that sin 55^circ - sin 19^circ + sin 53^circ - sin 17^circ = cos 1^circ