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Prove that the function f(x)=tanx-4x is ...

Prove that the function `f(x)=tanx-4x` is strictly decreasing on `(-pi//3,\ pi//3)` .

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Given,`f(x)=tanx−4x`
⇒`f′(x)=sec^2x−4`
When `−π/3​ Therefore,
`1 < sec^2x < 4`
⇒`−3<(sec^2x−4)<0`
Thus for `−π/3 ​< x < π/3`​,f′(x)<0
Hence f is strictly decreasing on `(−π/3​,π/3​)`.
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