Question

If
`cos(x) = (3)/(4)`, what is the value for
`cos(x + \pi )`?

Answer 1

`\textit{Sum and Difference Identities} \\\\ \cos(\alpha + \beta)= \cos(\alpha)\cos(\beta)- \sin(\alpha)\sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cos(x)=\cfrac{3}{4} \\\\[-0.35em] ~\dotfill\\\\ \cos(x+\pi )\implies \cos(x)\cos(\pi )-\sin(x)\sin(\pi ) \\\\\\ \cos(x)\left( \text{\LARGE -1} \right)-\sin(x)\left( \text{\LARGE 0} \right)\implies -\cos(x)\implies -\cfrac{3}{4}`