mostre que cos ø/cos 2ø é = 1/cosø + sinø

Tem certesa que essa é a pergunda certa?

\(\[\begin{align} & \frac{\text{se}{{\text{n}}^{\text{2}}}\left( \text{ }\!\!\theta\!\!\text{ } \right)}{\text{sen}\left( \text{ }\!\!\theta\!\!\text{ } \right)\left( \text{1}\text{-}\text{co}{{\text{s}}^{\text{2}}}\left( \text{ }\!\!\theta\!\!\text{ } \right) \right)}\text{-}\frac{\text{1}\text{-}\text{co}{{\text{s}}^{\text{2}}}\left( \text{ }\!\!\theta\!\!\text{ } \right)}{\text{sen}\left( \text{ }\!\!\theta\!\!\text{ } \right)\left( \text{1}\text{-}\text{co}{{\text{s}}^{\text{2}}}\left( \text{ }\!\!\theta\!\!\text{ } \right) \right)} \\ & Logo: \\ & \frac{\text{se}{{\text{n}}^{\text{2}}}\left( \text{ }\!\!\theta\!\!\text{ } \right)\text{+}\text{co}{{\text{s}}^{\text{2}}}\left( \text{ }\!\!\theta\!\!\text{ } \right)\text{-}\text{1}}{\text{sen}\left( \text{ }\!\!\theta\!\!\text{ } \right)\left( \text{1}\text{-}\text{co}{{\text{s}}^{\text{2}}}\left( \text{ }\!\!\theta\!\!\text{ } \right) \right)} \\ & Por\tan to: \\ & \text{se}{{\text{n}}^{\text{2}}}\text{(f)=(1+cos(f)(1-cos(f))=1-co}{{\text{s}}^{\text{2}}}\text{(f)} \\ & \text{multiplicamos por sen(f)(1-cos(f))} \\ & \text{Logo:} \\ & \text{se}{{\text{n}}^{\text{2}}}\text{(f)+co}{{\text{s}}^{\text{2}}}\text{(f)=1} \\ & \\ \end{align}\] \)