Answer:
1-2*sin^2 (x) = 2cos^2(x) -1
Step-by-step explanation:
1-2sin^2(x)
= 1-2(1-cos^2(x)) =2cos^2(x)-1; Pythagorean identity, sin^2(x)=1-cos^2(x)
=1-2+2cos^2(x)=2cos^2(x)-1; distribute
= -1+2cos^2(x)=2cos^2(x) -1; collect and rearrange terms
= 2cos^2(x)-1 = 2cos^2(x)-1
