Question

Se sen x= m e cos x = n, determine sen 2x, cos 2x e tan 2x em função de m e n

Answer 1

$\bullet\;\;\mathrm{sen\,}2x=2\,\mathrm{sen\,}x\cos x\\ \\ \boxed{\begin{array}{c} \mathrm{sen\,}2x=2mn \end{array}}$


$\bullet\;\;\cos 2x=\cos^{2}x-\mathrm{sen}^{2\,}x\\ \\ \boxed{\begin{array}{c}\cos 2x=m^{2}-n^{2} \end{array}}$


$\bullet\;\;\tan 2x=\dfrac{\mathrm{sen\,}2x}{\cos 2x}\\ \\ \\ \boxed{\begin{array}{c}\tan 2x=\dfrac{2\,mn}{m^{2}-n^{2}} \end{array}}$