could some one help me out?

Question

how can I proof that( sine alpha + cos alpha) <= 1/2, using the fact that sine (- beta) and cos (-beta) = cos beta?

Answer 1

try alpha = 0 degrees plug that in to get

sin0 + cos0 = 0 + 1 = 1> 1/2

just one counterexample disproves the "identity" An identity must be true for all angles

-1 < sinA+ cosA < 1, not 1/2

also sin(-B) does not = cosB

sin(-90) = -1 which doesn't equal cos90 = 0

cos(-90) = 0 though which equals cos90

sin(-90) + cos(-90) doesn't equal cos90 either