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Prove that f(theta)=(4sintheta)/(2+costh...

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

Text Solution

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given:` y=frac(4sintheta)(2+cos theta)`
The derivative of y is `(8costheta+4)/(2+costheta)^2`
For y to be the increasing function, the derivative of y should be positive.
`(8costheta+4)/(2+costheta)^2>=0`,
`impliescostheta>=-1/2`
For `0<=theta<=pi/2`, `costheta` is positive . Therefore y is increasing function for `0<=theta<=pi/2`
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