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# where#n∈Z#
graph{(sinx)^2+2cosx-2 [-0.92, 19.08, -5.48, 4.52]}