Shat that \(\tan ^ { 2 } x + \operatorname { co } { } ^ { 2 } x \equiv \sec ^ { 2 } x + \frac { 1 } { 2 } \mathrm { co } 2 x - \frac { 1 } { 2 }\) ach n e fid b ex ct le 6
$$\int _ { 0 } ^ { \frac { 1 } { 4 } \pi } \left( \tan ^ { 2 } x + \cos ^ { 2 } x \right) d x$$
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Th regn en lo edy th cn \(y = \tan x + \mathrm { co } x\) ad th lin \(\mathrm { s } x = 0 \quad x = \frac { 1 } { 4 } \pi\) ad \(y = 0\) is sw n in th d ag am.
Fid th ex ct m e \(\mathbf { 6 }\) th sb idpd ed wh n this reg n is ro ated cm p etely abt th \(x\)-ax s.
If B e th follw ig lin dpg to cm p ete th an wer(s) to ay q stin (s), th q stin \(\mathrm { m } \quad \mathbf { b } \quad \mathrm { r } ( \mathrm { s } )\) ms tb clearlys n n