Question

cos2a+cosa=0

Answer 1

Use the trig identity:\[\cos 2a=2\cos ^{2}a-1\]
\[2\cos ^{2}a-1+cosa=0\] Substitute x= cos a

2x^2-1+x=0

Solve for x and you get x=1/2 and -1

Substitute cosa=x back.

cosa=x
cosa=1/2
a=pi/3, 5pi/3

Substitute cosa=x back for the other value of x.

cosa=x
cosa=-1
a=pi

So your answers are:pi/3, pi, 5pi/3

Answer 2

Don't forget to fan. :P

Answer 3

Thank you !