Question

solve cos θ + cos^2θ =0

Answer 1

Answer:

cos x + cos 2x = 0

find x

[cos 2x = 2 cos²x - 1]

by substituting this, we get

cos x + 2 cos² x - 1 = 0

let cos x be y

=> 2y² + y - 1 = 0

=> 2y² + 2y - y - 1 = 0

=> 2y (y + 1) - 1(y + 1) = 0

=> (2y - 1)(y + 1) = 0

=> 2y - 1 = 0 and y + 1 = 0

=> y = 1/2 and y = -1

when y = 1/2

1/2 = cos x, therefore x = 60° or π/3

when y = - 1

-1 = cos x , therefore x = 180° or π