B bing.thio New member Joined Mar 20, 2020 Messages 1 Mar 20, 2020 #1 My question is regarding number 24! How can you manipulate the (1-sin^2(t)) term into a (1-cos(2t)/2 term?

My question is regarding number 24! How can you manipulate the (1-sin^2(t)) term into a (1-cos(2t)/2 term?

tkhunny Moderator Staff member Joined Apr 12, 2005 Messages 10,671 Mar 20, 2020 #2 One for free. This is why we study trigonometry before we study differential equations. cos(2t) = 1 - 2sin^{2}(t) sin^{2}(t) = [1 - cos(2t)]/2 ..........................edited Better brush up. It doesn't get easier.

One for free. This is why we study trigonometry before we study differential equations. cos(2t) = 1 - 2sin^{2}(t) sin^{2}(t) = [1 - cos(2t)]/2 ..........................edited Better brush up. It doesn't get easier.

S Subhotosh Khan Super Moderator Staff member Joined Jun 18, 2007 Messages 20,882 Mar 20, 2020 #3 bing.thio said: View attachment 17304 My question is regarding number 24! How can you manipulate the (1-sin^2(t)) term into a (1-cos(2t)/2 term? Click to expand... use cos(2t) = cos^{2}(t) - sin^{2}(t)

bing.thio said: View attachment 17304 My question is regarding number 24! How can you manipulate the (1-sin^2(t)) term into a (1-cos(2t)/2 term? Click to expand... use cos(2t) = cos^{2}(t) - sin^{2}(t)