Question

identificaciones trigonométricas

Answer 1

1.)
${tanx.ctgx-sen^2x=}\\\\{ \frac{senx}{cosx} \times \frac{cosx}{senx} -sen^2x=}\\\\{1-sen^2x=}\\\\{\boxed{cos^2x}}$

2.)
${senx.ctgx=}\\\\{\frac{senx}{1} \times \frac{cosx}{senx}=}\\\\{\boxed{cosx}}$

3.)
${ \frac{1}{1-senx} =}\\\\{ \frac{1}{1-senx} \times \frac{1+senx}{1+senx} =}\\\\{ \frac{1+senx}{1-sen^2x} =}\\\\{ \frac{1+senx}{cos^2x} =}\\\\{ \frac{1}{cos^2x} + \frac{senx}{cos^2x} =}\\\\{sec^2x+ \frac{1}{cosx} . \frac{senx}{cosx} =}\\\\{\boxed{sec^2x+secx.tanx}}}\\\\{4.)}\\{secx(1-sen^2x)=ctg.senx}\\\\{secx(cos^2x)=\frac{cosx}{senx}.\frac{senx}{1}}\\\\{\frac{1}{cosx}.\frac{cos^2x}{1}= cosx}\\\\{\boxed{cosx=cosx}}\\\\{5.)}\\{(senx+cscx)^2=}\\\\{sen^2x+2senx.cscx+csc^2x=}\\\\{sen^2x+2(1)+csc^2x=}\\\\{sen^2x+2+(1+ctg^2x)=}\\\\{sen^2x+2+1+ctg^2x=}\\\\{\boxed{sen^2x+ctg^2x+3}}\\\\{\mathbf{salu2.!!\ :)}}\\{\mathbf{Wellington}}$