Question

Find the intervals in which f(x)= (sin 3x - cos 3x), 0

Answer 1

we have to find the interval of x in which function f(x) = (sin3x - cos3x) = 0

or, sin3x - cos3x = 0

or, sin3x = cos3x

or, tan3x = 1

or, tan3x = tan(π/4)

or, 3x = nπ + π/4

hence, x = nπ/3 + π/12

if n = 0, x = π/12

if n = 1 , x = π/3 + π/12 = 5π/12

if n = -1 , x = -π/3 + π/12 = -3π/12 = -π/4 and so on

hence , x $\in\{\frac{n\pi}{3}+\frac{\pi}{12}\}$ where n belongs to integers.