Trig identity proof

[AlexDoesMath]

Need steps to complete proof of this identity.
(sin t - cos t)^2 = 1 - sin (2t)

 

[Deleted member 4993]

Need steps to complete proof of this identity.
(sin t - cos t)^2 = 1 - sin (2t)

Start with

(a - b)^2 = a^2 + b^2 - 2ab

 

[Otis]

… (sin t - cos t)^2 = 1 - sin (2t)

Hi Alex. After you apply the pattern that Subhotosh provided (to carry out the multiplication on the left-hand side of your equation), the next step is to look at your list of trigonometric identities and see what you could substitute for the expression sin(t)^2 + cos(t)^2.

Please show any work that you've tried, if you'd like more help.

?