How do I solve the following equation step by step?

-sin^2x=2cosx-2

1 Answer
Apr 8, 2018

x= 0+2pin where n∈Z

Explanation:

-sin^2x=2cosx-2

  1. Set the equation equal to 0
    -sin^2x-2cosx+2=0

  2. Apply the modified Pythagorean identity: 1-cos^2theta=sin^2theta:
    -(1-cos^2theta)-2cosx+2=0

  3. Simplify by distributing
    -1+cos^2x-2cosx+2=0

  4. Combine like terms
    cos^2x-2cosx+1=0

  5. Factor like a quadratic
    (cosx-1)(cosx-1)=0

  6. Solve
    cosx=1
    x= 0+2pin where n∈Z

graph{(sinx)^2+2cosx-2 [-0.92, 19.08, -5.48, 4.52]}