Solve the equation for x if 0 ≤ x < 2π. Give your answer in radians using exact values only. (Enter your answers as a comma-separated list.) sin x + cos x = sqrt2

Answer 1

Hi Madison:

Here's how to handle this one.

sin x + cos x = √2

(sin x + cos x)² = 2 [squaring both sides

sin²x + 2 sin x cos x + cos²x = 2

1 + 2 sin x cos x = 2 [sin²x + cos²x = 1

2 sin x cos x = 1

sin 2x = 1 [double angle formula: sin 2x = 2sin x cos x

=> 2x = π/2 [π/2 is the only angle in [0, 2π) with a sine value of +1

x = π/4