Question

Lim (2 cos^2 2x - 2 sin^2 2x) / (sin 2x + cos 2x) x--> 3π/8?

Answer 1

limx→(3π/8) (2 cos²(2x) - 2 sin²(2x)) / (sin 2x + cos 2x)
limx→(3π/8) 2(cos²(2x) - sin²(2x) / (sin 2x + cos 2x)
limx→(3π/8) 2(cos(2x) - sin(2x))(cos(2x) + sin(2x)) / (sin 2x + cos 2x)
limx→(3π/8) 2(cos(2x) - sin(2x))
= 2(cos(6π/8) - sin(6π/8))
= 2(cos 135° - sin 135°)
= 2(cos(180-45) - sin(180-45))
= 2(-cos 45° - sin 45°)
= 2(-½√2 - ½√2)
= -2√2

Answer 2

Manipulasi aljabar.