Prove that the minimum value of `3 cosx+4 sin x + 5 ` is 0.

The minimum value of 3cosx+4sinx+8 is

The minimum value of f(x)=3cos x + 4sin x is ………..

The minimum value 4^(x) + 4^(1-x), x in R is

If 0ltxlt(pi)/(2) , then the minimum value of 2(sinx+cosx+cosec 2x)^3 is

Let X be the soultion set of the equation A^(x)=-I, where A = [[0 , 1, -1],[4, -3, 4],[3, -3, 4]] and I is the corresponding unit matrix and x subseteq N, the minimum value of sum ( cos ^(x) theta + sin ^(x) theta ) theta in R - { (npi)/2 , n in I } is

Find the absolute maximum value and the absolute minimum value of the functions in the given intervals: f (x) = sin x + cos x , x in [0,pi]

Prove that = (sin 5x - 2 sin 3 x + sin x)/( cos 5x - cos x) = tan x

sin x + sin 3x + sin 5x =0

Find the maximum and minimum values of x+sin(2x) on [0, 2pi] .