How do I solve the following equation step by step?
-sin^2x=2cosx-2
1 Answer
Apr 8, 2018
Explanation:
-
Set the equation equal to 0
-sin^2x-2cosx+2=0 -
Apply the modified Pythagorean identity:
1-cos^2theta=sin^2theta :
-(1-cos^2theta)-2cosx+2=0 -
Simplify by distributing
-1+cos^2x-2cosx+2=0 -
Combine like terms
cos^2x-2cosx+1=0 -
Factor like a quadratic
(cosx-1)(cosx-1)=0 -
Solve
cosx=1
x= 0+2pin wheren∈Z
graph{(sinx)^2+2cosx-2 [-0.92, 19.08, -5.48, 4.52]}