I need help proving trigonometric identities. Most of my difficulty lies in actually factoring the equation. For example, one of the problems is (cos t - sin t)^2 + (cos t + sin t)^2 = 2. I have to prove that the left side is equal to 2. How do I do that?
LS = (cost - sint)^2 + (cost + sint)^
= cos^2 t - 2sintcost + sin^2 t + cos^2 t + 2sintcost + sin^2 t
= 2cos^2 t + 2sin^2 t
= 2(sin^2 t + cos^2 t)
= 2(1)
= 2 = RS