Question

the expression negative 1 plus tangent x over 1 plus tangent x can be rewritten as which of the following

Answer 1

`\tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \qquad \tan(\alpha - \beta) = \cfrac{\tan(\alpha)- \tan(\beta)}{1+ \tan(\alpha)\tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{-1+\tan(x)}{1+\tan(x)}\implies \cfrac{-1+\tan(x)}{1-(-1)\tan(x)} \\\\\\ \cfrac{\tan\left( (3\pi )/(4) \right)+\tan(x)}{1-\tan\left( (3\pi )/(4) \right)\tan(x)}\implies \tan\left( \cfrac{3\pi }{4} + x\right)`