Find all solutions to the equation.

cos2x + 2 cos x + 1 = 0

Here, the given expression is,

 ( Because cos(2x) = 2cos²x-1 )

Thus, 2 cos x = 0 or cos x + 1 = 0

If ,

⇒

⇒

⇒

Where, n = 0, 1, 2, ......

Now, if,

⇒

⇒

Where, n = 0, 1, 2, ......

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: