Prove that `f(theta)=(4sintheta)/(2+costheta)-theta` is an increasing function of `theta` in `[0,pi/2]` .

Explanation

Given,`f(theta)=(4sintheta)/(2+costheta)`

`f'(x)=(8costheta+4)/(2+costheta)^2`

For y to be increasing function , the derivative of y should be positive.

=`costheta≥−1/2`

For` 0≤theta≤π/2` , `costheta` is positive.

Therefore y is increasing function for `0≤theta≤2π​.`