A curve `C_1` is defined by : `e^x cos x` for `x in [0,2 pi]` and passes through the origin. Prove that the roots of the function y = 0 (other than zero) occurs in the ranges `pi/2 < x < pi and (3pi)/2 < x < 2 pi.`

Writhe the range of the function f(x)=cos[x],\ w h e r e-\ pi/2

Prove that the function are increasing for the given intervals: f(x)=secx-cos e cx ,x in (0,pi/2)

Prove that the function are increasing for the given intervals: f(x)=secx-cos e cx ,x in (0,pi/2)

Prove that the function are increasing for the given intervals: f(x)=secx-cos e cx ,x in (0,pi/2)

The maximum value of the function f(x) = sin (x+pi/6)+ cos (x+pi/6) in the interval (0, pi/2) occurs at

The number of non zero roots of the equation sqrt(sin x)=cos^(-1)(cos x) in (0,2 pi)

If x in(0,1), then greatest root of the equation sin2 pi x=sqrt(2)cos pi x is

A function is defined by f(x) = int_0^pi cos t cos(x-t)dt,0 <= x <= 2 pi then which of the following equals?

Prove that the function f given by f (x) = log cos x is strictly decreasing on (0,pi/2) and strictly increasing on (pi/2,pi) prove that the function f given by f(x) = log sin x is strictly decreasing on ( 0 , pi/2) and strictly increasing on ( pi/2 , pi) ..