Exercício sobre trigonometria

Resolver as equações:

$\phantom{X}sec^2\,x\,=\,2\,\centerdot\,tg\,x\phantom{X}$

$\phantom{X}\dfrac{1}{sen^2\,x}\,=\,1\,-\,\dfrac{cos\,x}{sen\,x}\phantom{X}$

$\phantom{X}sen\,2x\,\centerdot\,cos(x\,+\,\dfrac{\pi}{\,4\,})\,=\,cox\,2x\,\centerdot\,sen(x\,+\,\dfrac{\,\pi\,}{4})\phantom{X}$

$\phantom{X}(1\,-\,tg\,x)(1\,+\,sen\,2x)\,=\,1\,+\,tg\,x\phantom{X}$

resposta: a) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{4}\,+\,k\pi\,\rbrace\,$
b) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{2}\,+\,k\pi\;$ ou $\;x\,=\,\frac{3\pi}{4}\,+\,k\pi\rbrace\,$
c) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{\pi}{4}\,+\,k\pi\;\rbrace\,$
d) $\,S\,=\,\lbrace\,x\,\in\,{\rm I\!R}\;|\;x\,=\,\frac{3\pi}{4}\,+\,k\pi\;$ ou $\;x\,=\,k\pi\rbrace\,$

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