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Question
Prove that `y=(4sintheta)/(2+costheta)-theta `
Solution
`y=(4sintheta)/(2+costheta)-0`
`dy/(d theta)=((2+costheta)(4costheta)+4sin^2theta)/(2+costheta)^2-1`
`=(8costheta+4cos^2theta+4sin^2theta)/(2costheta)^2-1`
`=(8costheta+4)/(2+costheta)^2-1`
`=(4costheta-cos^2theta)/(2+costheta)^2`
`dy/(d theta)=(costheta(4-costheta))/(2+costheta)^2`
for increasing `dy/(d theta)>0, theta epsilon(0,pi/2)`
`0<= costheta<=1`
(2+cosθ)2 always greater than 0
So, `dy/(d theta) `
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