4cosx = -sin^2 x+4

Question

Write your answer in radians in terms of pi

Answer 1

Substitutes the main pythagorean identity sin^2 = 1 - cos^2

4 cos = -(1 - cos^2) + 4

Then, upon distributing the negative.....

4 cos = -1 + cos^2 + 4

Everyone to the right side:

0 = -1 + cos^2 + 4 - 4 cos

Combines .Like .Terms (CLT:

0 = cos^2 - 4 cos + 3

Factors: you can let z = cos, upon which the equation

becomes z^2-4z+3 = (z-3)(z-1)

0= (cos - 3)(cos - 1 )

Then cos - 3 = 0 or cos-1 = 0

SO then cos = 3 or cos = 1

However the cosine CANNOT be 3. It MUST

be between 1 and -1. So this branch is a dead end.

But cos=1 --> x=0

Yes, it checks