true or false: The equation sec^2 x - 1 = tan^2 x is an identity.

Question

anonymous · Answer

In mathematics, an "identity" is an equation which is always true.

solomonzelman · Answer

$\large\color{black}{ \displaystyle \sec^2 x - 1 = \tan^2 x  }$


$\large\color{black}{ \displaystyle \frac{1}{\cos^2 x} - 1 = \tan^2 x  }$


$\large\color{black}{ \displaystyle \frac{1}{\cos^2 x} - \frac{\cos^2 x}{\cos^2 x} = \tan^2 x  }$


$\large\color{black}{ \displaystyle \frac{1-\cos^2 x}{\cos^2 x} = \tan^2 x  }$


$\large\color{black}{ \displaystyle \frac{\sin^2 x}{\cos^2 x} = \tan^2 x }$


$\large\color{black}{ \displaystyle \tan^2 x = \tan^2 x  }$