Question

Which is a value of 60 = cos(x + 10)?

Answer 1

`\displaystyle \sf sin(60^\circ) = cos(x+10^\circ) \\\\ \text{we now that} : \\\\ sin(90^\circ-\theta) = cos(\theta) \\\\\ therefore : \\\\ sin(90^\circ-30^\circ) = sin(60^\circ) = cos(30^\circ)\\\\\\\ \text{So}: \\\\ cos(30^\circ) = cos(x+10^\circ) \\\\ 30^\circ = x+10^\circ \\\\ \large\boxed{\sf \ x = 20^\circ\ }\checkmark \\\\\ \text{or } \\\\ x = 20^\circ +2\cdot k \cdot \pi \ \ \ ;\ (k\in \mathbb{Z} )`