Show that tan−1(cos(x))>π4cos(x) for every

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manpreet Tuteehub forum best answer Best Answer 3 years ago

 

This is something I made up like that only. Show that

tan1(cosx)>π4cosxtan−1⁡(cos⁡x)>π4cos⁡x

for every x(0,π/2)x∈(0,π/2)

 

My method was that both are convex in given interval so we can just compare area under curve.

A2=π4π/20cos(x)dx=π4A2=π4∫0π/2cos⁡(x)dx=π4
A1=π/20tan1(cosx)dx=12144" class="texatom" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 16.65px; vertical-align: 0
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