Question

cosA + cos2A + cos3A = 0

Answer 1

cos A + cos 3a = 2 cos 2a. cos a
Therefor:
cos A + cos 3A + cos 2A = 2cos (2A).cos A + cos (2A) =
= cos 2A(2cos A + 1) = 0.
Either factor should be zero:
a. cos 2A = 0 --> unit circle --> 2 solutions
2A=π2+2kπ, and 2A=3π2+2kπ
1. 2A=π2+2kπ --> A=π4+kπ
2. 2A=3π2+2kπ--> A=3π4+kπ
b. (2cos A + 1) = 0 --> cosA=−12
Trig table and unit circle give 2 solutions:
A=±2π3+2kπ
−2π3 is co-terminal to 4π3.

Answer 2

Step-by-step explanation:

$\frac{n\pi}{2} + \frac{\pi}{4} \: and \: 2n\pi + \frac{2\pi}{3}$