Show that|sinx−cosx|≤√2 for all x. (Use the table below)

Question

x 0 π/6 π/4 π/3 π/2

sinx = 0 √1/2 √2/2 √3/2 √4/2

Answer 1

|sin(x) - cos(x)| ≤ √2 = 1.414

x = 0 |0 - 1| = 1 < √2

x = π/6 |π/2 - √3/2| = 1 < √2

x = π/4 |1/√2 - 1/√2 | = 0 < √2

x = π/3 |√3/2 - 1/2 | = .366 < √2

x = π/2 |1 - 0 | = 1 < √2