Question

Verify the equation is an identity cos (180 - x) = - cos x Show Work plzzz!!!

Answer 1

check your Unit Circle for the values of at 180°

$cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ cos(180-x)=-cos(x) \\\\[-0.35em] ~\dotfill\\\\ cos(180^o-x)\implies cos(180^o)cos(x)+sin(180^o)sin(x) \\\\\\ (-1)cos(x)+(0)sin(x)\implies -cos(x)$