Question

solve:
cos2x+cosx =0 for 0 12 years ago

Answer 1

Is that a cos squared of x or a cos of twox?

Answer 2

\[\cos2x=2(cosx)^{2}-1\]
use it to make a quadratic in cosx and then solve

Answer 3

abhi: going to try rishabhjaiswal's suggestion? It's a very good one.

Answer 4

and how to make a quadratic in cosx

Answer 5

You're starting with cos2x+cosx =0, or (cos2x)+cosx =0.
I put the cos 2x term inside parentheses because we're going to make a substitution, the one suggested by rishabhjaiswal. (See above)

Answer 6

We get, by substitution,
\[(2(\cos x)^{2}-1)+ \cos x=0.\]

Answer 7

Removing the outer parentheses:\[2(\cos x)^{2}-1+(\cos x)=0.\]

Answer 8

Rearranging, \[2(\cos x)^{2}+(\cos x) - 1 = 0.\]

Answer 9

Note that this looks very much like the quadratic equation 2a^2 + a - 1 = 0.
Please solve this quadratic equation in a. (We'll return to the previous equation, in (cos x), later.)

Answer 10

this help me a lot thank you