Exercício sobre trigonometria

Resolver as equações:

$\phantom{X}sen\,x\,\,-\,\sqrt{\,3\,}\,\centerdot\,cosx\,=\,0\phantom{X}$

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

$\phantom{X}tg\,x\,+\,cotg\,x\,=\,2\phantom{X}$

$\phantom{X}sec^2\,x\,=\,1\;+\;tg\,x\,\phantom{X}$

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

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