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 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 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 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) =__________.

If x cos alpha + y sin alpha = x cos beta + y sin beta = 2a then cos alpha cos beta =

If x cos alpha + y sin alpha = x cos beta + y sin beta = a, 0

Given 3sin beta+5cos beta=5, then the value of (3cos beta-5sin beta)^(2) is

If alpha, beta are the roots of x^(2) - 3x + a = 0 , a in R and lt 1 lt beta, then find the values of a

lim_ (x rarr0) (e ^ (ax) -cos alpha x) / (e ^ (beta x) -cos beta x)