Determine whether the statement is true or false.
-cos 135° = cos 225° cos 90° + sin 225° sin 90°

Question

Quizplus · Accepted Answer

This statement is true because it is an application of the cosine angle addition formula, $\cos(\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$, with $\alpha = 135°$ and $\beta = 90°$, which simplifies to $\cos(135° + 90°) = \cos 135° \cos 90° + \sin 135° \sin 90°$. Given that $\cos 90° = 0$ and $\sin 90° = 1$, the equation simplifies to $\cos 225° = \sin 135°$, which is true since both sides equal $-\sqrt{2}/2$.

Determine Whether the Statement Is True or False